Hotel Arkanchi (Lonely Planet spells it Arqonchi) is in a great location within the walls of the Old City of Khiva, right behind the historic madressa which is now Hotel Khiva.
It is nothing fancy, but quite adequate and good value for money. In the wooden main building the rooms appear to be all of differing sizes. Although I had booked a single, I had a huge room with three beds in it. The bathroom was big enough to have a party in too. The heating was excellent, which was a definate plus as it was really cold for March outside.
There are what appeared to be newer rooms of a uniform, smaller size and concrete or stone construction in the courtyard.
Breakfast was included in the US$25/night price. It too was nothing special, but adequate.