BU does have some pleasant, quiet areas. The river bank is a beautiful place to hang out. However, as has been noted, BU is not just in Boston. Boston and BU overlap and intertwine. Its border with the river is the sharpest demarcation between BU/not BU, but even that is tricky because BUs boathouse is on the opposite side of the river from the rest of the buildings. A very wide avenue--more than six lanes in some places--with trolley lines in the middle of it runs through BU.
BU admissions can be weird. The why BU? essay is very important as is showing up for a tour/info session not too late in the admissions season. Adding on a visit to a specific school/college is even better. They don't want a student who is looking for a way to go to school in Boston. They want someone who knows that BU is the best fit. My daughter was surprised to be waitlisted by BU while being accepted by much more selective schools. I think being a local student didn't help, but she didn't show the love as much as she could have either. She already knew BU well, and even has BU credit on her HS transcript, so she didn't do much on campus for her application. I can see that BU could have thought she viewed it as a safety.
BU is not known for generous aid, but I don't have experience with that.
I don't know of any homeschoolers going to BU, but I have never heard that homeschoolers are at a disadvantage in applying there.