I used Baku Tours by Baku Explorer and I am very pleased and happy with them. We did the old town walking tour, breakfast, mud volcanoes, Gobustan and dinner. This is a local business and not a big company - I do strongly believe that local businesses should be supported and I am really glad I chose them.
Highly recommended. The guide Dunyamin was very keen on showing and explaining everything. The tour was not limited to history, but also included politics, literature, etc.
I did several tours: the free walking tour, Mystic Ateshgah and Yanar Dag, Candy Mountains, and Gobustan and Mud Volcanoes. Everyone that was part of this company truly care for their guests and all worked very hard to make sure I was comfortable and saw what I wanted to see. Highly recommended - you won't go wrong with Baku Tours!