If you have 2 days to spend in Barnard Castle, we recommend visiting the Bowes Museum, which houses a collection of European fine and decorative arts. It will take about 2-3 hours to explore the museum.
You can also visit the Barnard Castle ruins and the eponymous town, the former of which will take less than an hour to tour. Additionally, you can walk around the River Tees and enjoy the natural beauty of the area.
If you have more time, you can take a trip to High Force Waterfall, which is about 30 minutes away by car, and spend 1-2 hours there.
There are several options for places to stay, including The Three Horseshoes Inn, The Old Well Inn, and The Morritt Arms Hotel. Each offers a unique experience and is highly rated by visitors.