I'm looking for a good solid-body electric guitar that has a nice jazz sound. I'm looking for the classic 0 treble with a poppy bass sound (hopefully that makes sense). Any suggestions?
I find that naturally brighter sounding guitars with humbuckers with the tone rolled off can get some really nice jazz tones. Look at some teles with humbuckers in the neck.
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About everything that has maple in it.
(tops or bodys)

e.g. PRS´ and LPs have maple tops.
"Black gives way to more black."

I have UG Black Style and I can barely read my signature.

Also, I like black.

Gibson Les Paul, the solid body jazz guitar
2003 Music Man Axis Pacific Blue Burst
I had an Ibanez Artist that would sounds very good in a jazz setting. I highly recommend them, simply because everyone thinks others first, so you can get them for sometimes less. I still regret selling that guitar. It was a special one to me. I was able to get a good John Scofield type sound out of it, even though he plays a semi-hollow.
A Les Paul, Les Paul Doublecut or a PRS Custom 22. The regular humbuckers could work okay, though I think you might be better off with some P-90 pickups instead. Just remember to roll the tone knob down a bit because most classic jazz tones were created with guitars that were at least semi-hollow and a solid body guitar is going to need to have it's tone controls rolled down at least a little to get close to that.

Whatever you end up going for, try to aim for a thick body with a lot of body mass. Pickups should be very low output with decent clarity but not Fender style singlecoils - humbuckers or P-90s will be what you want (P-90s will be a touch clearer, but they can become victims of 50/60hz cycle hum). Whatever you get, you might want to consider having the existing control pots changed to high-quality 250k pots for both volume and tone controls (most guitars with humbuckers or P-90s will come with 500k pots, which give a brighter tone).

As far as getting punchy bass goes, that's more down to your amp and speakers than the guitar.
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For a cheaper Jazz guitar, I suggest to you the Grestch Pro Jet...

It's got a bigsby, great jazz sound, and if you ever want to, you can shred with it. 'Nuff said. Price, $700.

An Epi 1956 Les Paul Gold Top would probably be nice too. The 50's were the age of Jazz, and it comes with P90's. On top of that, I think they're only like $500 or $600.