It’s best you monitor your utility costs in Boston carefully, as it’s one of the more expensive places in the country for renters to live. For example, a one-bedroom apartment can range from around $1,000 to $1,800 per month while a two-bedroom rental can be leased anywhere from around $1,500 to $2,500 monthly.ven if you share an apartment, the cost of renting doesn’t seem to go down too much, as average rental rates for roommates range from about $700 to $1,000 per month. Therefore, you have to budget appropriately for utilities. Major utilites in Boston include electricity, natural gas, the Internet, phone and Cable TV.