In winter there's a lot of, mostly Turkish, ski tourism and the rest of the year a lot of day trips from Istanbul and tours. However, I would not consider Bursa a 'tourist town'. The Ulu Mosque with a marvellous interior. The market complex starts right behind the Han's. When you are at Muradiye, it's worth to visit the Kultur Parki, especially on a Sunday afternoon.
Turkish families go here for a day out.
Lovely lanes and ponds where you can row or water pedalling. Nice tea houses and little stands who sell al kinds of goods. Nice terraces nearby with a splendid view over parts of the city and valleys. The Sakarya Caddesi, every taxi driver knows it, or ask for 'Arap Sukru'. A small street lined with little restaurants and wine shops.