I think the most interesting sections are above the Rappahanic River on the Western Shore and the Choptank, on the Eastern. But there are a lot of places south of there, especially on the Western side.
The season, without a heater on board would be from April/May through October/November.
As Jeremy suggested, there are places a in the Southern Bay you could look at.
I know the Neuse from long ago when a friend had a boat there. I'm sure it nice. We just are spoiled in the Chesapeake for so many neat gunk holing ops.