Lower blue is class 3ish (maybe class 3-) in summit county. It's a fun run, a bit easier than Shoshone but still worth checking out. That would be my top pick for a follow-up to shoshone.
Pumphouse is running too, but it's only a class 3-/2+ with a heckuva lot of flatwater in between the 2 canyons that have all the rapids. There are a lot of other runs I would much rather go on!
south canyon (below shoshone) is a class 2+ish run, but a lot of places to play. It's a fun run, though pretty dang easy.
Shoshone is pretty short... of course you could always just run it over and over to your heart's content too
I dunno about any nearby class 4 runs that are running right now.
Hope that helps!