Walking the historic ‘Freedom Trail’ is my suggestion - you can ether go on a guided tour or print out a map and do it on your own. Here’s a link: http://www.thefreedomtrail.org/book-tour/
If it is a nice day, I would also include walking down Newbury Street and into the Public Garden. It is great for shopping and people watching plus it is pretty. If both of you are really strong walkers, you can expand that into walking through Beacon Hill and into downtown. Boston is extremely compact and walkable so you can see a great deal in just a few miles if you start at upper Newbury in the Back Bay and work your way as far as you want into downtown and possibly into the North End if you want to get some good Italian food.
This may sound strange, but I’ll recommend the Mt. Auburn Cemetery. In early May it’s at its peak beauty, and the birds you’ll see there - especially warblers - are just amazing.
All suggestions are great. Let me add this: a guided tour through ‘Boston on Foot’. I have a friend who has just undergone rigorous training including massive amounts of studying and writing papers all to be able to volunteer! to lead tours. here’s a link:
My first thought was Newbury Street and the Public Gardens. You could have a nice lunch a long the way. If either of you are baseball fans, I loved taking a tour of Fenway Park.