Welcome Andrew,
I went to college in Petersburg, and use to live in Prince George off River Rd by Fort Lee.
As always the Appomattox River is always a good place to start. Especially during the spring up by the little power station off of Grove Ave. You can find the shad, herring and striped bass/rockfish plentiful in the small rapid moving water...crappie, smallmouth and largemouth bass also can be caught from the same general area by the little pedestrian bridge where the water is more calm, there are some deeper pockets. Caught fish for years!
Heading down river a little in Old Towne Petersburg behind the Crocker Spot restaurant, you park on the gravel right by the old railroad tracks. Then just follow the path through the trees and come to a wide pipe that you can walk across (only can do this at low-tide)...then you get to a bunch of clear out spots on the bank and you have reached "Catfish Alley) which is on the Appomattox but is like a 50-60 hole....HUGE catfish, bass, bream, gar fish can all be caught.
But for some smaller ponds or hidden gems, Dance's Sporting Goods is the place to go. They can point you in the right direction and also more knowledgeable in that area. Good luck buddy!