If you are traveling to Boston and do not plan to visit any region outside of the Boston area you do not need to rent a car. Not renting a car will save you money and keep you on a budget. Boston is a great city to use the MBTA or T train (subway). Children under the age of 12 ride the subway FREE of charge. You can get a weekly card for $19 that gives you unlimited usage of the T train (subway) and the inner harbor ferry service. There is a harbor ferry service that runs from Logan Airport to Downtown Aquarium to the Charlestown Shipyard. We took the Harbor Ferry and enjoyed getting to see Boston from the water. My son really enjoyed riding up top of the ferry, even though it was raining! The T train runs from Downtown Boston to outlying areas such as Cambridge.
Boston is very compact so you can walk the city easily. We walked the Freedom Trail the afternoon we landed in Boston. It is very simple, just follow the colored pathway. The Freedom Trail is 2.5 miles long and has 16 historic sites along the trail. There are maps all around town or you can download an app for the Boston Freedom trail. We just used a map. We prefer the north end of the Freedom Trail. The north Boston neighborhoods are very quaint and historic.
If you have a rental car, as we did the day we flew in to Boston you will have to deal with parking in Boston. Parking is VERY expensive! Parking near downtown Boston in June 2014 was $35. Remember I am a budget conscious traveler? No way I am going to pay $35 to park. I found the Nautica Parking Garage near the USS Constitution museum (five minute walk) for $12 for 4 hours. If you take your parking ticket to the museum they will validate it and save you some money.
Driving in Boston is insane as well. We found the streets to be in disrepair. Drivers drive wherever they desire. Frequently drivers would be driving along the shoulder of the road. Our GPS redirected us through the warehouse district and we found potholes as big as the hood of our car! If you rent your car from Logan Airport you will have to pay a toll to go through the Ted Williams Tunnel ($3.50 in June 2014) or you will have to go the long way to get to Boston which in traffic could take you 45 minutes - 1 hour.