I would definitely check out the North Hills area to get a good taste of a cool area to shop and dine.
http://www.google.com/url?sa=t&rct=j...50165853,d.eWU
I have not been to the Durham Farmer's Market but I love the State Farmer's Market in Raleigh
You may want to visit the Brier Creek area as there are a lot of homes, shopping, restaurants.
Since you have kids you may want to consider checking out Pullen Park. It's a fantastic park and we had our daughters 1st birthday there.
If you're interested in what Malls have to offer for the area you should definitely check out Southpoint which is an indoor/outdoor mall with a lot of style.
If you can squeeze in a quick picnic you could head of to Jordan Lake for some fun.
Depending on the weekend you are here the Durham Bulls could be playing in town so if you are interested in baseball you should check them out. That particular area of Durham where they are located is called the American Tobacco District and it has great entertainment and restaurants. My wife and I love Tyler's Taproom which is across from the park.
American Tobacco Campus Web Site
If you're into Soccer we have a semi-pro team based out of Cary called the Carolina Railhawks. You could catch a game if they are playing. This place is extremely kid friendly and the team is rather fun to watch.
These are just some things off the top of my head, I hope you can at least get to one of them.