Your trip to Mombasa City cannot be complete without visiting the Fort Jesus. As UNESCO puts it, it's one of the most outstanding and well preserved examples of 16th Portuguese military fortification and a landmark in the history of this type of construction.
Besides history, there are plenty of other things to see and do in and around Fort Jesus. You can explore the narrow streets of Mombasa Old Town, enjoy the beautiful scenery, try out local cuisines, etc. You can also get a bird's view of the ocean right from Fort Jesus.