Lodging in Japan isn't necessarily that expensive. Camp Zama is, pretty much, in the suburbs of Tokyo MAP, so most of the more upscale choices will be in Tokyo or Yokohama which are both within commuting distance.

The great majority of foreigners who'll stay at that particular Odakyu (it forms part of a respected chain) will be there on Camp Zama business.

Last person to ask about the area:
http://www.flyertalk.com/forum/showthread.php?t=684839
(from what I could work out, staying in Ebina is probably most convenient, but you might be better off in Machida if you expect to spend your evenings in Tokyo)