I was an undergraduate at Emerson College, so I had a few friends who lived over in Beacon Hill, and I've met grad students who live there as well. There are some studios you may come across, but they are by no means a steal and the size of the apartments in Beacon Hill aren't comparable to the bigger apartments you could find outside of downtown. The apartments I've seen in Beacon Hill are small. My friend lives in a studio there right now with her boyfriend and the rent is around $1,200.00 for the studio. They have a kitchen, bedroom, and bathroom. It is small, and older, but for one person would be great. The only problem I have with Beacon Hill is moving in. I helped my friend move in, and let me tell you moving furniture up 5 rickety flights of stairs was not pleasant.
I lived in a dorm close by on Arlington Street back then, and it was awesome to live in the neighborhood, it is clean, the safest you can get for downtown Boston, and now the Whole Foods is within walking distance so groceries are easy to buy.
Would I live in Beacon Hill?
Yes I would.
Do I think I can afford it?
No.