Okay, the edit on height and inseam really helps narrow it down.

You'll be limited on bikes on the used market for sure - but not completely out of the picture.
Mountain bike frame size will be "extra small" or 14" or so. Road/cyclocross/hybrid frame size will be 45cm or so, which is extremely hard to find, if at all.
This bike is a possibility, in the "extra small" size http://www.bikesdirect.com/products/dawes/lttour.htm
This one pushes your budget boundary, but is a solid basis for future upgrades: http://www.konaworld.com/bike.cfm?content=dew


An immediate possibility pops up - mixte style frame, which is a unisex frame that is quite stylish and practical:

Ebay might be the best source for these, and the sweet spot would be 1960's and 70's european manufacturers such as Raleigh and Peugeot.

http://cgi.ebay.com/VINTAGE-NISHIKI-...item5d29e7f062
http://cgi.ebay.com/Bugatti-Touring-...item2c55b12709