We advise that you plan to spend some time checking out the different areas and applying for apartments. Please note that when renting an apartment, you are often required to pay the first month's rent, last month's rent, and/or security deposit when you sign the lease. As a rough guide to what this means to your checkbook, studios and one-bedrooms in most areas go for around $1,000-$1,700 per month. If you're willing to share, you can find reasonable places for $500 and up.
If you use a realtor, you may also be required to pay a realtor fee (see Realtors and Realtor Fees).
||Allston, Brighton, Jamaica Plain ("JP"), Fenway, Brookline, Beacon Hill, the Back Bay, South End, South Boston (different from the South End; the western edge, near the Red line) are the most convenient locations. Many parts of Cambridge, Somerville, and Newton are all convenient to the Longwood Medical Area. But most of Greater Boston is accessible, if you don't mind adding 20-40 minutes to your commute.
(FYI: All of the names above are names for areas of Boston, except for Newton, Brookline, Cambridge and Somerville, which are different towns with separate administrations, school districts, etc.)
When you're choosing a place to live in there are a number of factors (outside of the rent) that you will need to consider:
Walking Distance to Work
If you want to walk to work you should probably look first in Brookline and the Fenway (JP, the Back Bay, and the South End are also possibilities)
If you have children, especially of school age, you should look first at Brookline and Newton, where the public school systems are excellent (but apartments are expensive)
Student and Metropolitan Lifestyles
Those looking for areas oriented towards a student lifestyle should try Cambridge, Somerville and Allston first. For a metropolitan lifestyle, try Beacon Hill, the Back Bay and South End.
If your priority is the maximum space for the money, try Brighton, Allston, South Boston, and Somerville.
If you like a racially diverse, pro-artist, pro-veggie and gay-friendly communities Jamaica Plain and the South End are the best bets. Some bits of Cambridge also have this character, e.g. Central Square, Cambridgeport, and Inman Square.
Another factor to consider when choosing housing is the safety of the neighborhood. If you're thinking of living in an area that looks as if it could be dubious, the local police station should be able to give you an idea of the number and type of incidents in your area. Two areas close to the Medical School that have historically been rather unsafe but now appear to be in transition are Dorchester and Roxbury. Jones Hill in Dorchester (bordered by Columbia Road and Uphams Corner to the west, and Stoughton, Pleasant, and Hancock streets to the north, east and south) is getting a lot of press lately as the new hot neighborhood, particularly for economic refugees from the South End.
Public transportation is a very important issue, especially since you are unlikely to be able to drive to the Medical School (parking is essentially unavailable except in exceptional circumstances). If you're near a T stop, get familiar with where your line goes (see http://www.mbta.com). The closest stops to HMS are Longwood Ave (Green Line, D branch) and Brigham Circle (Green Line, E branch). Therefore, being on the B and C branches of the Green line is much less convenient for commuting to work than being on the D and E branches. (There is no A branch -- it used to go to Brighton but has not been operating for at least 20 years.) Check that you can get to grocery stores, etc. conveniently. Buses (also at http://www.mbta.com) and the Harvard shuttles (especially the M2 shuttle: see http://www.masco.org) are also worth checking out.
To Park or Not to Park!
Different towns have surprisingly different personalities when it comes to parking. Brookline has NO on-street parking overnight (even if you're a resident), so you essentially can't keep a car in Brookline unless your apartment comes with a parking space. Many other towns have large areas of "resident parking only", a sure sign that on-street parking will be difficult. But the resident parking stickers are usually free or very cheap.