You can easily do a city tour yourself. In fact, unless the layover was forced onto me (ie, I had no choice but to book that way) I'd definitely not try to wrap my planes around using the free tour/hotel.
With the Sultan having scared away half the tourist crowd, hotel prices at prime locations are as low as never before. IST is easy to navigate by public transport. The hotel that IST would place you is near the airport and almost all of them are unconvenient to get into the city. The city tour, while OK, is definitely not something for the individual travellers that likes to explore stuff themselves.