There is a newly built park next to a library that is beautiful. It also is in a social district and has on tap beers and ciders.
For any shopping needs, near the hotel there is a Harris Teeter, Target, and various restaurants that you can walk to from the hotel. There is also a Coldstone for the Icecream lovers.
Go visit the city where Tanatswa grew up. Their downtown is full of beautiful history and very good food.
If you are a flower lover, Duke Gardens is beautiful in late summer and early fall. This could be a nice spot to visit if you arrive to the Triangle area early.