By junior year, moving off of the South 40 becomes a very attractive option for most students. Besides fraternity members, who often choose the cheaper frat house option, most upperclassmen decide to find an apartment in a nearby residential area, either through University subcontractors like Quadrangle Housing and Apartment Referral Service, or through a private realtor. University City seems to be the most popular area, with several streets such as Kingsbury Boulevard, University Drive, and Kingsland, Pershing, Washington, and Waterman avenues populated almost entirely by students. There are centrally located apartments east of Skinker Boulevard and north of Delmar Boulevard as well that are less popular but have generally cheaper rent. The Wash U-owned apartments like Greenway tend to be more expensive than privately owned ones, but they have the benefit of amenities like Ethernet, laundry rooms, and package utilities. Plus, the advantages of not having to spend weeks knocking on doors looking for apartments, calling realtors, and later dealing with unhappy surprises from your landlord ("Oh yeah, I forgot to tell you, the roaches here have dune buggies.") are worth considering.
There is fierce competition for the choice apartments, of course. Many are owned by Wash U, so your lottery number and those of your roommates will be decisive in whether or not you get something through the Wash U housing process. For the private route, the key is to first find someone living in an apartment you like who will be leaving next year (either by word of mouth, or by knocking on doors). Get them to sign a sheet saying they'll turn over the lease to you at the end of their contract, and you're set. Many apartments are handed down from friend to friend this way, but there's always the old-fashioned door-to-door option, which has been known to work on occasion.