1) would start out with a Duck Tour which is an orientation tour which will take you throughout the city of Boston. The Duck Tour is the most popular attraction in the city so be sure to get there early so you don't get put on the waiting list for the later ducks. However, if you find yourself on the waiting list and board at the Museum of Science, you can at least walk through the Museum while you wait.
2.) If you want a great view have dinner or drinks in the Top of the Hub restaurant which overlooks the city. Beautiful at night.
3.) Freedom Trail. If you like history or just want to take a genuinely awesome walk throughout the city the Freedom Trail starts in Boston common and takes you through Fanuiel Hall, Quicy Market and the North End (amazing Italian food, Canolis--you name it) and if you want, you can continue on to Charlestown for the rest of the trail. I warn you though it's a little long and if you're only going to be in town for the weekend, you might want to stop at the North End
4.) Newbury Street! Newbury Street is a must see even if you just want to have lunch on one of the outside tables--it's a must for people watching and shopping, too. The Museum of Fine Arts is a few stops away from Copley on the E-line. Great place to go after Newbury Street--the museum is huge and well worth the money to see all the great artists captured inside.
5.) I'd also pick up a Go Boston Card while you're in town which is good for attractions like Duck Tour, MFA, Freedom Trail attractions, etc. It's great to get a weekend card and just check out all the attractions in the city for a lower price