You could stay in Providence, Rhode Island, and take the commuter rail up to Boston for the day.

Or some of the historic towns around Boston that are on the commuter rail might be affordable. But probably not Salem in October, unless it's early October.

There are also campgrounds within range of the T and commuter rail, including Bumpkin Island in Boston Harbor. But October is risky for cold weather - it's not unusual to get snow just before Halloween.