Bond park off high house rd allows fishing from anywhere you can reach. The pond there is stocked with cats, also has bass, carp, and bream. On the back side of the spillway the creek wanders for a while before leaving the park, but I have no idea if there are fish there; it's pretty skinny.
If you really want moving water you might have to head west on 64 past Jordan lake and hit the haw river, or pick it up below the dam in the southern part of the county. Crabtree creek and the Neuse river to the northeast also have fishable water altho the Crabtree area is undergoing PCB cleanup.