I once stayed for a few months in Coimbatore for some research work I had to do in this region. The city itself is very industrial and has nothing much to see. There is an amazing university with a botanical garden (TNAU), a smallish stadium in which you can go for walks, good cotton material shops and an amazing dance school for bharatanatyam. But the surroundings of Coimbatore have some amazing nature to see, as well as a pompous Isha Yoga Center. From Coimbatore you can reach Ooty, a lovely hillstation.