Anyone can buy property in the US. For internationals, cash is best.
There are fees associated with your purchase. Typically there are condo fees to maintain your investment and these vary depending on the amenities or what the homeowner;s association has decided they want to cover. They can cover the ocncierge, hot water, heat, snow removal as examples.
In addition, there are property taxes and these vary depending on the square footage and area you are buying. Property taxes help the community you are living in. A portion goes to the local schools, streets etc.
In Cambridge, the rental market is very expensive so it may be best to own instead or rent and not having anything to show. When you leave you can continue to rent it out or sell it so you have not lost money.
I can send you last years market report and 2012 Q1 market report so you can see the average price and locations.
Please send me youe email and I can send them to you. I can be reached at email@example.com.
Hope this helps!