How do you enhance a bad listening room's accoustics without breaking the bank? thoughts?

I haven't read all the repsonses but some were right. The connection of your speakers to the floor is the number one culprrit. Sound travels faster through solid objects than air. You can try Iso Acoustics for that issue or build you own isolation platforms for the speakers

Yes interior acoustics will have benefit to tamming a reverberant environment which neighbours can hear, but it won't stop most of what they hear. Interior acoustics is mostly for your listening benefit.

REW is a tool, it does NOT tell you how to deal with acoustic issues, only experience & knowledge does. I've been designing rooms for over 2 decades and it has become a key offering in my audio business. Apart from buying some used acoustic treaments, there's no inexpensive way of getting a room to sound great.

effective materials cost money today even if you DIY. Learn about acoustics and what really works from a physics stand point, there are too many pretenders out there. Vicoustic seem to have the best price performance and WAF

Gary / audio by di tomasso .ca

It seems to me that your main concern is not upsetting your neighbours. Very honourable and most considerate of you . . BRAVO ! Cork will definitely not do the trick, The only real solutions - sorry but true - top class headphones OR sell up and move. Question - I wonder if your neighbours are as considerate as you most definitely are. VIVA LA MUSICA

If it is sound isolation you are after, you want to have a high STC rating (sound transmission class) for wall and floor construction.   
Currently the IBC required code minimum STC for a condo is 50.
An STC of 75 is preferable .
The primary ways of achieving a higher STC rating are mass, isolation &  attenuation.
I also live in a condo and am considering working on two walls, the wall I share with my nieghbor and the entrance wall to the corridor. Maybe with the construction of a sound isolating partition. But this takes space......

The best room treatment for me was done by accident!

My parents had a very dense hand-woven wool rug that they didn’t use anymore. Cost them around $5-6k and is beautiful so I didn’t want to get rid of it. It was nearly the size of my listening room so I put down a large felt pad on the wood floor and then placed the rug over that. It replaced a basic polyester rug that covered maybe half the floor. Immediately the sound softened and its was just the listener and the speakers.

Otherwise chairs and a couch in the room, but this rug seems to have stopped reflections very effectively.

Want a good room?  Most Tx  look gross and do little.  They are expensive. Also, tx stuck on the wall don't do much.  They have to be suspended from the wall.  Oh, no body told you that, huh. 

First, use your brain.  How many reflections do youi want left.  Do you want to listen to your system or your room.  That's what I thought.  Take your room out of the picture.  Get Eco-core 2x4 panels (the best) and make 4x8 from them. Mount them on 4x8 x1" foam insulation panels from Home Depot.  Cover with your preference. Suspend them from the ceiling 4-6" from every wall.  If you don't have line array speakers, do the ceiling also.  Carpet the floor.  Even dirt sounds better than wood or tile.  Get some sono-tubes for tube traps.  Stick them in the corners and tune for the frequency that is bad for your room. 

And if you loose your dog, ask yourself why he always goes in that room to sleep.