If you're staying a couple days, I love what's called the 'back bay' area.
The prudential observatory gives you a great view of the city. Newbury street has some funky shops.
I would also recommend using the trolley
service. It's a little pricey, but less than a cab and less intimidating than the subway. The drivers are very knowledgable and tourist oriented.
tour is another great way to see a lot of the town in a short time.