This is a flat, wide, open-air, raised trail with beautiful views along the Eno River, part of NC's famous Mtns to Sea Trail. There are historical markers along the walk and it's great for people watching. About 3 miles total.
A beautiful park scattered with art surrounds the NC Museum of Art, which is free to enter the permanent exhibits. It has one of the world’s largest collection of Rodin’s bronze statues and is a good picnic spot if the weather is nice. It makes sense to stop here if you’re coming from RDU as it’s close to the airport; otherwise, it’s half an hour from The Colonial.
Take it from an alum, Duke Gardens has something for everyone! It's free to visit and there are plenty of nice spots for photos or to just sit and relax. Maybe enjoy a picnic, study/do some remote work if you have to. This address will take you to the parking lot.
One of the oldest and largest planetariums in the country, a former astronaut training ground and current gem of UNC. See the website for information on planetarium shows available, updated monthly. There may not be a show that fits in the weekend’s schedule, but you can still visit the museum during business hours anytime for free.
For American-style casual fare: J&F Kitchen; for cheap, fresh, delicious, authentic Mexican food: La Restaurante Ixtapa or Los Altos (the latter is on the same block as The Colonial); for modern American fare in a classy setting: The Nomad at The Osbunn (also on the same block). Napoli Pizzeria Hillsborough makes wood-fired, Neopolitan-style personal pizzas and is the most highly rated restaurant in town. It's a 14-minute walk from The Colonial or a short drive from either hotel.