The dessert restaurant mentioned above is called Finale, and there is another branch of it in Park Plaza (Arlington stop on the green line) which would be closer to you if you are staying downtown.
In the North End, my personal pick would be Pomodoro if you want something casual. They have good fried calamari, and their pastas are tasty. They don't take reservations and the space is very small. If you want something more upscale, Prezza is excellent. It is expensive, and they do take reservations. Carmen is another good choice, though again it is very small.
For seafood, you really can get good seafood at a lot of places in Boston--you don't have to go to a seafood specific place. Legal's fish is very good and fresh, but their side dishes are kind of boring, and the atmosphere is just OK.
Finally, if you do go to the Union Oyster House, make sure to sit at the bar. If you sit in the restuarant part, the oysters are pre-shucked.