You can find relatively cheap (around $9 or $10) in the city on weekends. Try the Best Parking app or something like that to find inexpensive lots around the area(s) and time you would you like to go. I personally prefer taking the subway into the city, but the frequency of service is less on the weekends (and in particular on Sundays), so you may find it easier and/or more convenient to drive.
Agree with Legal Harborside. It is right on the water and while Legal is essentially a chain now, this is somewhat of a unique location for Legal, in that it is divided into three levels, each with a different feel.
Regarding tolls, I believe you can go on the Mass EZ-Pass site and calculate toll costs based on where you are travelling.