In this area, $1,000 can't find you a 1 bedroom/1 bath condo to rent!
Your best bet is to work with property management companies and their rental agents in the areas where you want to find a rental.
Too many scammers (and a lot from out of the country) find listings for sale and pass them off as their own places to rent. You can drive by the place and see if there's a for sale sign. Then call the listing agent and ask if it's for rent. Chances are that it's not.
Good luck to you.