I would definitely go to the Gardner Museum. If you're into art, the MFA is also good. If you like history the USS Constitution and Cassin Young are interesting and Bunker Hill is nearby. JFK Library is interesting and unique to Boston. I would recommend taking the ferry to George's Island if the weather is good. Also walking/biking the Esplanade is nice if the weather is good.

Sarma is my favorite restaurant; you should try to get a reservation, but they do accept walk-ins, so you could try early/late on a week night. Otherwise I like Gustazo, Tres Gatos, Noah's Kitchen, and Row 34. Dumpling House isn't far from Harvard and it's one of my favorite Chinese restaurants. If you're looking to fill some time you should try candlepin bowling; it's unique to New England. Enjoy your trip and happy birthday!