Jordan Lake, Falls Lake and Shearon Harris are big lakes and accessible by boat, but also have bank fishing access points. Bond Park lake in Cary, Lake Pine in Apex, Lake Lynn in Raleigh, Umstead park has a few lakes. Alot of them are mentioned in past threads on here, read a few pages back and I am sure you will find more on each of them.
I fish Jordan on foot and it can be tough to be productive there without a boat, you really have to hunt to find good shallow water structure. I've had good luck with channels on the Haw river, some nice bass in there too. Small lake at Umstead can be nice for bass at times.
Harris Lake is my favorite. Clean water, quiet and lots of fish. It doesn't get the pleasure boaters that Jordan does. If you're on foot you might try some of the subdivision lakes and ponds. You might be surprised at the size of the bass you catch. I've found that if you look like you might belong there and don't stay too long you can fish just about any body of water you can find in Cary and Apex
I fish south Jordan often and have never been to Harris, I'll have to check it out this weekend. I got a kayak a bit ago that I'll have to take out and see how it is. And you're right about the time/belonging part. I've fished a decent amount of small ponds around commercial and residential areas and haven't been bothered, but I usually only stay about 30 mins.