If I was an out-of-state resident, then the choice between the three would probably be difficult; I would probably choose whichever is cheapest or whichever location I like the best. However, I probably wouldn't go for Drexel just because of all of their financial issues... but anyway.
If you're in-state for a medical school, then I don't think that you should go out-of-state unless:
1) You really need a change of scenery
2) The out of state school is much better (ranked higher, has better opportunities, whatever)
3) Personal reasons (significant other, etc.)
Drexel and Finch, reputation-wise, definetely are not better than Albany. If anything (and I just KNOW i'm going to get bad karma for this), I would say that Albany has a better reputation because the other two are frequently seen as last-choice private schools for those that weren't accepted into their state schools. I'm sure that plenty of people will attack me for saying this, but it really is ture.
So, unless the OP has major issues with going to Albany, I would say go to Albany.