The Copley Place Garage (that's the one they referred to) Is in the same building complex as the Westin, so it's a short, indoor walk once you find a parking space.

The Sheraton-Lexington is a decent place that's an easy, 10-minute highway drive to Alewife T station. The Newton Marriott is a relatively nice place that's a 3-minute drive to the Riverside T station. (However, the Riverside T station is at the end of the Green Line - a fairly long and slow T ride to Boston compared to other lines.) Both of them have free parking.

Among lower-quality places, there are Holiday Inns in Newton (adjacent to Riverside T station) and in Somerville/Charlestown (next to Sullivan Square T station). The Sheraton-Newton is not an especially pleasant place to stay, but it does have good access to bus service that goes into downtown. (Though parking at the Newton might not be free.)