I like all the suggestions made so far. Sara P Duke Gardens makes for a grea walk. Never been to a Canes game but hear they are lots of fun.
Restaurant wise all of the suggestions made so far are great choices. One other place I recently tried in Durham is
Dos Perros. It is a nice Mexican Restaurant (they take reservations) in the heart of downtown. It is a little pricey (dinner entrees are $16-$22) but the food is excellent and they have an
outstanding rare beer list if you are into beers.