Accomodations available in Israel cover the full spectrum of options. For more information please see: http://goisrael.com/Tourism_Eng/Items/Accommodations.htm
Most of the Israeli web-sites for private rentals, etc. are in Hebrew, however, you might want to take a look at some of the online english speaking groups, such as Tanglo, at Yahoo groups for Tel Aviv and Janglo at janglo.net for Jerusalem and see if you can post your request there, you are bound to get a variety of helpful suggestions.
best of look and looking forward to see you here soon.