I'm not just looking for chord progressions to improvise over, I'm thinking more, are there songs you know of that have solid rhythm that I could improvise over?

Most styles are fine.
take a song with a solo you like.
learn the rythm part
record yourself playing the rythm
improvise over it
Easy, look into a 12 bar blues shuffle. it's only 3 chords, and you can do a whole hell of alot over top.

Look into "tell me" by stevie ray vaughan. me and my friends dick around with that alot.
blue on black by kenny wayne shepard

its in D

have fun
My Gear
-Gibson Les Paul Studio
-Ibanez "lawsuit" Les Paul
-Ibanez S470
-PRS SE Custom

Marshall TSL100
Marshall 1960a cab

Dunlop 535q wah
Visual Sound Liquid Chorus