Originally Posted by JMN57

As you've settled on Boston, I'll toss in my two cents on some options (having gone to uni there in the 70s). There may be a # of things you want to do but consider:

1) going to Union Oyster House a block from Faneuil Hall. Oldest restaurant in Boston (1826) and you can sit at the oyster bar where Daniel Webster ate oysters by the bucket
2) if the weather is good, take the ferry or water taxi from Long Wharf across to Logan airport (either way)
3) the waterfront is a short and comfortable walk up to the State House and to the Boston Common
4) the bar that "Cheers" was modeled after is right next to the Common if you are so inclined.
5) if you like museums, the MFA is world-class
6) and if the Red Sox are playing (although unlikely there is a day game like the old days) and you're interested in attending an American baseball game it's a historic venue.
7) if you like Science, visit my alma mater - MIT
8) or you could visit that ratty school up the river and go to Harvard Sq.

Of course, do what pleases you and wishes that you have a great time!

ADDED: See that you're taking the 9AM in and 5PM out so time is scarce. If I were doing it, I'd water taxi or ferry either in or outbound, go to the waterfront, have lunch @ the Union Oyster House, explore around Faneuil Hall and the waterfront area and then head back to catch the flight. Given your flights, you get downtown 10:30 to 11AM and you'll have to leave around 3PM, latest 3:30 to safely get to the airport and negotiate security.