I was faced with a similar choice (LSU vs VCU) and I picked LSU mainly because of money and location. Since money isn't an issue for you, it makes it harder.
I like[d] New Orleans a lot more than Richmond (and this isn't a homer pick because I was DYING to leave this state), but VCU is a great school and I liked it more than LSU. I don't have anything to say about Tulane other than the hospital system is probably much better at VCU. I just found New Orleans to be a better city in many aspects. Richmond had a lot of the parts about New Orleans that I didn't like without as many of the good parts.