I'd like to enjoy some of Boston's nightlife. Where can I go with my aunt (they're in their early 40's, I'm 35), to listen to music, meet nice people and drink/eat? Most importantly WHERE is it safe to go. For example, Back Bay vs Quincy Market/Aquarium area? and House of Blues (Cambridge) vs Newbury Street?
How would you rate each of these places at night for safety. yes, providing we take precautions and am always aware of people around us.

As far as safety is concerned, all the areas you mention are perfectly fine. All these areas are popular places to go for tourists and locals alike. The "unsafe" areas of Boston are nowhere near where the typical visitor goes. Obviously, as you mentioned, use your common sense!
As far as places to go, what kinds of music do you and your aunts like?? House of Blues is fun. For local bands, the Middle East in Cambridge is very popular. Jake Ivory's on Landsdowne St (next to Fenway Park) is a fun piano bar--2 piano players taking requests and a bar full of people singing and dancing. It's one of my favorite places to go out. The Good Life is a popular place to hear music (Jazz I think-I havent been yet!). There are 2 locations. One in the Financial District, the other in the South End. A good website to check out music venues and other fun stuff is www.bostonphoenix.com or pick up a "hard copy" of the Boston Phoenix when you get in town-it's free and is found throughout the city. Have fun!!!

You probably already thought of this..but we REALLY enjoyed the Boston Pops!I hope to go sometime in the summer as the outdoor amphitheatre looks incredible!

Everything you've listed is as safe as the average american suburb. Boston is a very safe city.

I'd skip the House of Blues because it's a national chain. Landsdowne Street could be a good idea because there are so many clubs close to each other that if one is a dud you can move on (although then you're talking about paying multiple cover charges).

The Middle East is great for live rock bands

The Good life is popular enough that they've opened a third location in Central Square, Cambridge not far from the Middle East.

Newbury street is a fun place to walk around, but not known for its live music venues.

There's a club in the Faneuil Hall area called Trinity, where one level is live band, one is dance club and one is a plain old bar.

I think it's going to boil down to which type of music you like.

is it safe in Cambridge at night?

Rianna-
For the most part-yes. Just use common sense and you'll be fine!