The most cost effective way of touring Boston is a self-guided tour on the Freedom Trail: it's completely free. It does, however, require a lot of walking.

Here is what I would propose: rather than taking the Silver Line, which is relatively easy but takes you to South Station, which is not the best place from which to start, have your wife and MIL take the free MassPort shuttle bus to the MBTA subway station. Outside of baggage claim, they will find concrete pillars painted with blue stripes, where they will wait for a blue-and-white bus number 22, 33 or 55 for the 5-minute ride to the subway station. At the subway station, they can purchase a single ride ticket to Boston.

Tell them to follow the signs for the Boston-bound trains (they have to go through the turnstyle, up the escalator, across, and then down the escalator) for two stops to the Aquarium station. When they come upstairs (following the signs to the Aquarium), they will be very close to the Marriott Long Wharf hotel. This would be a great place for them to leave their bags (virtually any doorman at virtually any tourist hotel would be happy to check a bag for an appropriate tip) and to be picked up later in the day.

From the Marriott, they can either purchase a ticket to one of the tour buses (there are several that stop within a block of the Marriott), or can walk a couple of blocks towards the North End to pick up the Freedom Trail. (I'm sure the concierge at the Marriott can direct them; it's quite easy.)