The Good Pastor is right, Phoenix is in a large, flat valley with intersperced small foothills (which are actually mountain tops rising out of the aluvial soils that filled in the valley in earlier geologic times). You will be in a perfect spot for flatland riding. The Biltmore sits along the Salt River Project canal. As a result, you can do days of riding along the canal bike paths (both groomed gravel and concrete paths). Here is a great map of the canal system. BTW, the Biltmore is located along the canal at 24th Street.

http://www.srpnet.com/water/canals/distances.aspx

Regarding your mode of transportation, a MTB will probably be best. The canal paths from Pima west on either side of the Biltmore can be ridden on a roadish bike with at least 28mm tires. I've ridden that section many times on CX bikes with city tires. If you go east of Pima, you will be crossing the Pima Reservation, which is a little rougher than the west section, but very interesting. If you do go across the reservation, just be sure to carry plenty of water. There are no 7-11's on that side.

Please feel free to ping me if I can provide any assistance.

Ride on!