I forgot to mention that there are plenty of free/low cost things to do here. The weather is nice, so there's hiking, biking, etc. You can rent a canoe at Umstead state park for about $5, and they have free fishing equipment, organized nature walks, etc.
As bogart said, the museums in downtown Raleigh are all free, parking is free on weekends, and they are quite nice even by big city standards, especially the Museum of natural sciences. There is a fun "first Friday" concert downtown every month with art exhibits and bands.
There are many very low cost concerts and cultural events associated with the colleges and there's a pretty good music scene in general with each city having small venues in addition to the big stadium shows. Most college sports are also free (exceptions are basketball, football, and sometimes baseball.) We've gone with the kids to watch college soccer, baseball, hockey, and volleyball and had a blast.
Thrift shops abound, with the Goodwill at Brier Creek being my favorite because they keep it pretty clean and sort all of the clothes by gender and color and style. There are also a couple of large Durham rescue mission thrift shops (more dust bunnies there, unfortunately.) My friends like those because the clothes are also sorted by size. Those have the benefit of having a pretty high turnover of big ticket items such as furniture and even cars. There are some fancier consignment stores: The Stock Exchang have (women only) and Plato's Closet, for example.
There are multiple chain grocery stores (Food Lion, Harris Teeter, Kroger) as well as super WalMarts and Targets which sell groceries here and there. If you live anywhere near the RTP area you will have multiple options. My Mom always marvels at how much cheaper our groceries are than hers in Denver. Earthfare, Whole Foods, Fresh Market, Trader Joe's, Costco, BJ's Club, Sam's Club, they're all in the area.
If your kids are small, there are tons of free/very cheap things for them, like decent parks (one with a train and a carousel), NCSU sponsored "farm animal days" where they can hold baby chicks, a special children's museum called "Marbles", etc.
a great (but absurdly expensive) gourmet food store
I do love that place. One of my favorite things about Chapel Hill.