You can leave your car at most of the hotels in the Burlington area (except downtown in the parking decks) for free. The hotel lots are filled with Canadian cars all the time. The Canadians come down to Burlington to fly on vacation due to the cheaper air fares. They just stay a night in the hotel, leave the car, and take the hotel shuttle to the airport.

I'd stay away from the Park & Rides, there have been a number of cases recently were someone is cutting off the catalytic converters on cars there over night.