I may have missed if you said how long you'll be in the best city in the US (my opinion), but you may also consider venturing to some neighborhoods. I rarely go into downtown to eat, because there are so many fabulous restaurants in the neighborhoods near me. I live in Jamaica Plain (JP)--one of the neighborhoods that make up Boston--which has a "high street" with numerous restaurants. Most of them are easily accessible by foot, MBTA, or rental bikes that are available all over the city.
A few non-downtown recommendations:
1. La Morra (One of Tom Brady & Giselle's favorites) in Brookline.
2. Centre Street Cafe in JP has great breakfast, but often a line
3. Spoke in Somerville-I haven't been but have heard rave reviews from many friends
4. Cambridge Brewing Co in Kendall Square has an eclectic "locavore" menu and is one of the best craft breweries in the US.
5. Gallway House in JP is one of my favorites. It's a classic pub where all the locals go and the food is always great. If you have a car, parking is pretty easy.
http://www.bostonmagazine.com/best-restaurants-in-boston/
http://boston.eater.com/maps/best-boston-restaurants-38
Some tourist recommendations:
Boston Harbor cruise
Rent bikes and ride along the Charles River--there are paths on both sides and you can ride from downtown to Harvard Square, and further to Watertown and Waltham. It's a beautiful, flat ride with many options to turn around.
https://www.thehubway.com/ https://www.cityofboston.gov/bikes/share.asp http://trailmap.mapc.org/
Walk the Freedom Trail
Fenway Park/Red Sox
Go to the top of the Hancock Tower (the blue glass sliver building in Copley Square) now called 200 Clarendon
Walking: Copley Square, Newbury Street, Commonwealth Ave (the Emerald Necklace), Boston Public Garden/The Common, Beacon Hill, Rose Kennedy Greenway
Faneuil Hall and Quincy Market (tourist mecca)
Boston Public Market
Museums (Gardner would be my choice if you only have time for one)
I hope you have some time to enjoy Boston! What a great anniversary gift!