I like Somerville. It's more surburan than the other areas, so it's a lot cheaper. If you don't have a car, make sure you live off the T since the bus system is a real pain in the ass. Davis Square is nice and fairly cheap.
Beacon Hill is extremely pricey. Yeah,you're right near the college, but since Suffolk is located downtown, you're generally only a 15-20 minute T ride away anyway, no matter where you live.
The North End is generally expensive, but it's very pretty. Make sure to go to Mike's.
South End-thanks to gentrification it's gotten more expensive. There's some tension between the new residents and the old, although you'd probably never notice it. I just know because I did nonprofit work in the area.
Other areas to consider:
Brookline-safe,some areas are moderately priced,suburban
Fenway-Fairly close to downtown, some areas are moderately priced, a very nice blend of suburban and urban. I lived there for a number of years.
Cambridge-Price and safety varies from area to area. I lived in the "rough" part(between Harvard and Lechmere) and found it to be pretty safe, but loud. There were some kickass restaurants.
Allston/Brighton-In the BU area,loud, full of college students, but fairly cheap
Roxbury- Generally very cheap, can be rough and loud. I lived there for years and,personally, I think the "danger" factor is vastly overrated. I'm sure a number of other people would disagree.
East Boston- Seems sketchy, but it's very cheap. Stay away from the area near the airport.
Revere-the longest commute, parts of it are nice, parts of it are rough
Newton-Second longest commute,can be very expensive, very safe