Glad to hear you're going to be moving up into the area! If you're looking to live right in the city, then places like Allston, Brighton, Dorchester and South Boston are all great places to look. They are usually the most affordable, and will have a population with a similar age to you.
Allston & Brighton are out in the western part of the city by Boston College and Boston University, so there are a lot of college students out there which is good (at least I would like it). A good friend of mine got a great deal in Brighton and is directly next to a T-Station and is only about a 5 minute trip to the center of Brighton where all the bars are. The T will take you right into downtown if you want, it's cheap and about a 15-20 minute ride depending on where you're located. There's also decent parking, which is good if you have to drive to work. My friend drives to Framingham for work everyday, which is a similar distance to the city as Beverly, and he has no problem doing it. It's a really pretty neighborhood and is definitely worth checking out.
South Boston has a lot of recent college graduates. Where I'm from, Scituate (on the South Shore), the most popular place to get your first apartment is in South Boston. Lots of bars, which is great for partying and it's close to downtown Boston.
Dorchester is a large area, with a very diverse population. You will find some of the most dangerous areas in the city in Dorchester (or Dot as it's called by locals), but it also has some really pretty areas like Savin Hill and Dorchester Heights. I have a friend living in Dorchester Heights right now, and he loves it. It's right next to the JFK/UMass T-Station on the Red Line, and is about a 10 minute ride into downtown.
Other places you might want to consider that aren't in the city but are close are Somerville and Cambridge. I don't really know a lot about the areas b/c I haven't spent too much time in them, but I've heard good things about them. Like Shawn suggested before, check out the ArchBoston forum, they're a lot more knowledgeable about the area than I am.