Why Alexandria and what part of Alexandria? Arlington County, Alex, and Fairfax County are all confluent. The city of Alexandria is small, but the area referred to by many as Alexandria is much larger and actually part of Fairfax County. My fiancee teaches for Fairfax south of the Beltway. There are nice neighborhoods and not so nice neighborhoods near her school.
As for finding a place to live, look at Craigslist. There are many ads by individuals and apts. placed there.
My wife and I moved into Belle View condos about a month ago. We love it! It is a nice place, safe, and friendly (almost like Aggieland type friendly). The website for the community is: http://community.associawebsites.com/sites/BelleViewCondominium/Pages/AcwDefault.aspx