I'm not the best person to answer this, as I only spent less than 3 days in Doha in March. But I imagine it would be too hot to do anything outside, except maybe dune bashing. The Souq Waqif was okay, but not truly authentic. My favourite thing was the Museum of Islamic art - partly for the collection, which is different than the type of things you get in western museums, and includes the biggest jewels you've ever seen - but also for the building, which is a piece of art in itself, both from the inside and outside. But if you're looking for a beautiful city, authenticity, and some of the friendliest people you've ever met, you'd be better getting a connecting flight to Muscat