What to upgrade next?

If you wanted to make an upgrade which would be the next most noticeable improvement. 

1: Power Cord (currently just stock cord)
2: Power tubes (currently JJ's 2 each 300b)
3: Cartridge (currently running Denon 103R)

My system consists of Audion Silver Night Special Edition 300b integrated, Acoustic Solid TT, Zu Soul Superfly speakers with Mission cables. 

Costing absolutely nothing but time and effort, experimenting with loudspeaker and listener positioning can produce very positive results.  If you want to spend money you could look at isolation/resonance suppressing devices such as racks and footers.  Finally have you thought about the Zu version of the Denon cartridge?
Of the three choices you listed to me absolutely power tubes. You can do much better than JJ and the change in sound quality is  dramatic and substantial with better tubes. That being said ohhwy61 has some good thoughts above on positioning which is indeed free!
Yes we are in the process of changing our generic entertainment center to a custom walnut slab unit. Not necessarily specifically made for audio but it is very solid and wifey approved. The TT came with 3 point isolation pointed feet so hopefully that is correct isolation. I thought about the Zu version of that cartridge but they were out of stock a while back when I was looking into it. I've since come across SoundSmith and was wondering how much improvement that brand might bring in. I can move the speakers around a little bit but the location in our room is a bit limited. 

A vote for power cables.

I've gone through all kinds of upgrades--though always in a solid state mode. in upgrading components, clearly the biggest improvement was going from 80 watts to 200 watts, and again to 500 watt mono blocks. bigger impact that speakers, cd players, network streamers

in accessories, and i am still surprised at this, biggest improvement cape from power cables, better than speaker cables, ICs, digital cables, brass footers, maple plinths. The brass footers also made a big change, but only on my Cyrus cd changer, not on other components or my Marantz SA8004.

All of the upgrades improved things to various degrees, but the amps and the power cables were the biggest change.
Power cables made a big difference in my system too. But I also use 500wpc amps, so the 14awg cords that came with them, while acceptable, were definitely restricting the sound. I’m not sure if my experience with class d monoblocks will translate to your <10wpc tube amp.

Might I recommend vibration control as well? For the TT and integrated tube amp, spring suspended platforms will open up the sound and reduce the noise floor. I made my own from wooden platforms I cut to size and placed on top of properly spec’d springs. But there are plenty of commercial options as well.

Falling under vibration management, tube dampers can help improve your sound as well. I have a tube preamp that has a noisy power tube. Tube dampers dropped the noise coming from the tube noticeably and improved the sound of my system, so I decided to put some on all my signal tubes as well. That made a slight improvement, but not as noticeable as damping the noisy tube. But they’re very inexpensive, so it didn’t hurt to try.

With regards to tubes, I replaced all my stock Chinese tubes with better (but not TOTL by any means) modern Russian tungsols. In doing so, I noticed more of an improvement when I replaced signal tubes than power tubes.. but your integrated doesn’t have signal tubes, and I did notice an improvement with better power tubes, so that could be a good route.

Again, based on my experience with a decidedly different system, isolation platforms and cables made a bigger difference than tubes, unless your tubes are quite crappy.. I’ve had no experience with JJs, so I can offer no advice there.

Good luck!

I would get better tubes.  Most manufacturers include the JJ tubes because they are inexpensive.
What improvements are you looking for from the upgrade?  What phono stage are you using?  I build components and I use the JJ EZ34 in my power supply. It sounded better than any tube we tried in that position so don't just say that the JJ's won't provide the best sound.

Some good suggestions here but I would look into a phono stage.

Happy Listening.
What I am looking for is better separation and clarity and dynamics from the upgrade.
Yeah I forgot to mention the phono stage I am using is a PS Audio Nuwave. You just never know where the weak link is until you try something else. 
If i do decide to replace the tubes, I am pretty sure I will go with the KR300b HP. It's supposed to be their high performance tube made with top notch parts. 

I vote for tubes as well heres a good review of most of the new manufactures tubes. I like the gold lions as well run them in my 300b Finale audio F3008.


I vote for changing out the jj 300b,to anything else including used 300b's that are in your price range.Does this Intergrated use a 6922 and a 5687,if they are jj's I would look at changing them as well.

I would go after a better pwr cord as well,lots of good ones that don't hurt the pocket too bad.

Offcourse all the tweaks already mentioned usually provide good results too.

Your cartridge is a good one,if you really play a lot of vinyl maybe look at a upgrade in the future.

Just my 2 cents,

I find OP's question very difficult to answer. Different tweaks tend to result in improvements in different areas in sound quality. Some add a little more bass - my experience with good power cords, or give wider detail- my experience with cartridge, etc., etc. It really depends what specific deficiency in sound you're trying to alleviate. As for tube rolling, I have no experience in that space but I'm sure the same basic principles apply.
Power cords and what you will get out of them hinges on your interconnects and speaker cables, the better those are the more difference power cords makes.

In what I'd consider a reference grade system, meaning the interconnects and speaker cables are super high resolution and neutral, power cords can have jaw dropping differences. The guys that say they can't hear a difference have serious interconnect and speaker cable deficiencies, they are the guys that tried many budget cables and believe they have found "the best" cables for their system.

Cables are loaded with catch-22's, great speaker cable will reveal nasties in weak interconnects you couldn't hear before, yet I think you start with a solid known quantity there, and then do your evaluation work on interconnects. If you don't the work you do comparing interconnects means nothing because there is so much you will not be hearing that you need to hear.

I start with a good neutral speaker cable, go to interconnects starting with the source to preamp, then the preamp to amp. To me those who aren't willing to spend some money on interconnects should get an excellent integrated. Once you have a high degree of resolution power cords will knock your socks off. Once you have good power cords you will hear differences that are staggering between good ones and great ones.

Cable has got to be the most contentious thing in the audiophile world. As someone who has not only sold cable to hundreds of people, I have tried complete arrays of dozens of cable lines. Good cable has little to do with price anymore, but you do have to spend some money to get really good interconnects, just not extreme money. Power cords are a lot of fun to try once the other cables are really good, Not so much before that. Also the differences in tubes are staggering once the i/c's, speaker cable, and power cords are there. The better the power cords the bigger the differences you'll hear in tubes. I like well matched cryo treated, read reviews on your given tube type to get an idea what the different characteristics of the tubes are. Tubes are last after the system's resolution is good enough to hear very subtle differences.
Wow Aintitgr8 that makes sense. Maybe that's why I can't hear any difference between the $35 and $750 I.C.'s. I also tried a PS Audio AC12 power cord and there was no difference. The speaker cables I have are Zu Mission with the BU3 connector on the speaker end for a good solid connection. Maybe an upgrade to Zu Event may help or yet another brand of speaker cables. It's so hard to really know what is the bottleneck in the system. 
You already have a very nice system so I am surprised that no one has mentioned room treatments?

Before upgrading anything else, treat the reflection points in your listening space. Put some bass traps in the corners. There are some very simple DIY projects that don’t cost a lot of $$. You want to hang things that can absorb reflections.

I initially stuffed some large bean bag chairs into the corners behind my speakers to see if I could hear a difference (I could). But any large stuffed pillow could work.

As a test, you could also try hanging heavy velour curtains at reflection points to see what kind of effect (sonically) they have.

And play with speaker positioning.
You have to start out getting things good enough that you can hear differences in the things like power cords and tubes. At this point in my reference system changing power cords from one performance level to another is a no brainer to hear the differences. I have to be able to hear the difference between terminations and plugs from one type to another, it's what I do, so I can't help but try to help get someone asking a question like this get on the right track.

An upgrade of speaker cable resolution will allow you to hear interconnect improvements better. The source to preamp is going to make the biggest difference. Keep in mind that as you find cables that improve your system, that there are new levels to get out of further cable improvements. If you think modestly priced cables made a big difference stepping it up from there can make even bigger differences.
Power cables first, and as others have said that will reveal other deficiencies. ...And so it goes. Any effective change will be a revelation, and the next step is a function of what you upgrade first.

After upgrading power cables, my next step was an oversized PS Audio PowerPlant. That made an even more substantial difference. (I already had "good" interconnects, so those got upgraded to very good ones after everything else and now I am done for the time being...)