Some websites that might help you get an idea of pricing:
http://boston.craigslist.org/aap/
http://hotpads.com/
Some tips:
1)
You need 3-4 months' rent up front. Save up before you move there. You will need 1st month's rent, last month's rent, +/- deposit (another month's rent), +/- real estate agent's fee (another month's rent) = up to 4 months rent!
2)
A real estate agent will cost you a month's rent. Most landlords do not pay agent fees, but if you are limited by time (like, traveling from out of town for just a weekend to rent a place) it's really worth it -- craigslisting for an apartment will save you the fee but it much more stressful.
Expensive areas -- I'm guesstimating these figures off the top of my head but I think they are fairly "average" for 2 bedrooms:
- Back Bay ($2100+ and that may be underestimating)
- South End ($1800+)
- Beacon Hill ($2300+ and this is probably an underestimate)
- Cambridge ($1800+)
Less expensive alternatives:
- Allston/Brighton
- parts of Brookline
- Somerville ($1400+)
- Arlington ($1000+)
- Medford
The longer a commute you are willing to tolerate, the less money you'll pay in rent. Commutes do take longer for the same distance in Boston than in other parts of the country -- traffic is very dense.