There are numerous listings in your price range on Sheridan Road (5555 N. Sheridan, 6030 N. Sheridan, 6166 N. Sheridan, 6300 N. Sheridan, etc), Marine Drive (4880 N. Marine) and all of the streets near there (918 W. Winona, etc.). Edgewater is your best bet. You can either take the CTA train to the city or jump on Lake Shore Drive to get to downtown.
Best of Luck! :)