Entry Level Tube Integrated Amps

I think a PrimaLuna EVO 100 Integrated is a great starting point. 
 

Very good quality and built like a tank. It’s also easy to tube roll.

Vincent Audio has 2 models below $1000, look for B stock or open box. Not very tubey sound but that was just my ears, my speakers.

You could also get a preamp with tubes, my favorite pairing is tube preamp, SS amp.

@scotthiga   If you really want to experience what tubes are all about suggest you do a simple  SET integrated with a full range driver.

Check out Analogue Ethos.  You can do a kit or prebuilt. Beautiful cosmetics and I suspect great sounding as well. Other great options would be Erhard Audio, Elekit, AN kits, among others.   Pair that up with an Omega speaker (or similar efficient easy to drive design).

Certainly you could go with a push-pull tube design if you want something to drive your current speakers.  Just keep in mind not all speakers play well with tube amps. Synergy is key.  Otherwise, you could end up with something inferior to your current amp.  (BTW, it would be helpful if you post more info on your system. Otherwise, you will get many random opinions--including mine.)

Thanks for the many and interesting responses. I own Klipsch Heresy IV’s (99 dB sensitivity) and Omega DynaTen XRS’s (90 db sensitivity). On both speaker sets I’ve paired them with REL T9x subwoofers. Electronics on the Omega DynaTen XRS’s is a Naim Uniti Atom. The Klipsch Heresy IV’s are paired with a Technics SU-G700. Both systems use Maze Audio cables. Music is streamed (I don't own a turntable). The Klipsch Heresy IV's use a BluSound Node 2i for streaming. Thanks for your continuing commentary!

Nice.  Sounds to me like you have many options given those speakers and subs..  Now it would be good to know what kind of sound you are seeking.  What is it that your currents amps are not bringing to the table?  What kind of music do you enjoy and at what spl do you tend to listen?