If your daughter is into music at all, see if there is a concert at Symphony Hall. It’s a great venue!
Yes to the Freedom Trail. And don’t forget to walk through the public garden. You can do that when you go to Newbury Street.
One of my kids is a BU graduate and loved Boston. He absolutely hated NYU (loves NYC but hated NYU). So don’t assume your kid will hate one if they hated the other.
Yes, the T goes to the Northeastern campus, but really, we thought that campus had a self contained campus feel.
If you want to explore Boston, I would suggest not venturing to Portsmouth NH.
There are also tons of museums in Boston. If you like that sort of thing, there is something for everyone. We like the natural history museum.