Does anybody have any good suggestions for places to grab a bite or have a good meal in that area? Seems that none of the guidebooks I check come up with any good (but not too expensive) restaurants near the County Hall.

Well - it sounds like you must be reading old or useless guide books. There is a lot to see and do on the southbank and there are many places to eat w/i a short walk.

The Peoples Palace, the Archduke, the OXO Tower, Gourmet Pizza Co., two restaurants in the Tate Modern and a whole bunch of places a little farther down river.

meant to add - you will LOVE the location of the County Hall . . . . .

Don't feel you are confined to the South Bank -- some of those recommendations above are a pretty fair walk. You can cross the pedestrian Hungerford Bridge to Charing Cross and there is a huge range of places at your fingertips.

Thanks for the information. I'm starting to like the location of the County Hall more and more.