City wandering, Islamic Museum of Art, local city museums, National Library
Tips for other travellers
Try to stay in a local hotel.
I stayed at Al Najada Doha Hotel by Tivoli.
It was excellent - central, 5 star but affordable, great staff, all very obliging and helpful, handy to airport, central old city, close to all worthwhile attractions, the Souq, and all museums.
A $10 to $15 taxi ride to the newer, more touristic sites if youre missing the West.