There are so many wonderful things to do. You can walk the Freedom Trail for starters. Before you start make sure that you download one of the apps so you get some info while you walk. The Freedom Trail is amazing and you will have a chance to stop by some historical landmarks like Old North Church and the USS Constitution. One of the best parts is that it is free.
Here is a little bit more about what you'll be getting: The Freedom Trail is a 2.5-mile-long path through downtown Boston, Massachusetts, that passes by 16 locations significant to the history of the United States.
When the weather permits I like to go and explore the esplanade, these are paths along the Charles River. I usually try this late spring through the summer months and into early/mid-fall which is ideal to get the broadest palette of colors.
One thing that I did when I was younger was go to the Boston Public Library at Copley Square. It was a nice chance to catch my breath and it is really beautiful simply to walk around the area.
The same goes for Beacon Hill, mainly because it has a great historic neighborhood to explore.
You can also go to Harvard Square. For those of us who enjoy activities like exploring the shops this part of town is ideal. And of course you can visit Harvard campus over there.
This really isn't my type of thing. But my mother loves to visit Isabella Stewart Garnder Museum and I used to meet here there when she was in town. It was nice and there is a lot of history, plus $5 admission with a student ID, and when you are on a budget it might be a nice addition.
Then we have Boston Harbor (tea party anyone) and Faneuil Hall. Both of these are interesting to visit, and there are a lot of restaurants and cafes in the area so it can be nice fora couple of hours.
I'm a foodie so the North End is great since I love to eat Italian food and they have plenty of pastry shops, too. It can be great fun to explore the area with the intention on finding something tasty to eat. If you walk the Freedom Trail, North End is right at the end of the trai so it might be a nice way to end the day.