How many kings did Joshua conquer?

Joshua only conquered part of one land, although inhabited by various tribes or nations or 'people groups'(whatever term one prefers). Land areas outside of the land had already been conquered 'on the way in', such as what would now be termed as Northern Egypt and across the eastern side of the Jordan River in what is now the nation of Jordan. Moses was the leader of the nation at this time, prior to the entry into Canaan, although Joshua was his 'right hand man' in terms of military matters.

The land Joshua partly conquered was called Canaan, later Palestine, and today Israel.

The only cities which The Bible records that were destroyed by Joshua as part of this conquest were Jericho, Ai, and Hazor. The first and the last have evidence of significant destruction at around the relevant time period, as attested by Archaeology. The correct site of biblical Ai is still a matter of some discussion, although archaeologists know that materials were often re-used and sites scraped clean before rebuilding or reoccupation. So, no remains of what was only a small city anyway would not be surprising or relevant to the conquest as a whole.

It is also recorded that the Israelites were to 'live in cities you did not build'. This means that they were not coming to slash and burn with a scorched earth policy but to live in the land, which is why much was left intact. It is also recorded that they lived in tents for quite some years after the original occupation.

The main area of conquest by Joshua in the land of Canaan was along the central highlands.