Received 3 year AD to Boston University, University of Delaware, and Syracuse. Not sure which one to choose and not sure how I'm going to pay for my freshman year. Any advice on which school is best?
Congratulations on the scholarship awards. It's odd though that you didn't get a scholarship to your in-state school, but have instead two very expensive private schools among your choices. I suppose this means that Penn State may be extremely competitive even though it is a large unit.
You previously stated you already had been accepted at Penn State. I assume you would have mentioned it if you had gotten in at any of the other schools, so this makes your position a little tricky, especially since you don't know whether and how much aid any of them might offer. I don't remember when college notification occurs, but if it's on the same date in mid-March, then you'll have to make your ROTC decision in the absence of that information.
Have you visited the three schools and their AROTC units? You probably should contact the ROOs just to let them know you've received the scholarship but haven't been accepted to the school yet. Obviously, you can't tell each one that it is your first choice, but clearly you are interested. Also, you may want to explore with PSU whether there is a chance for a transfer. Is your heart set on Mount Nittany, or would other campuses like Altoona which also have ROTC be acceptable if it could boost your chance for a transfer?
All three are good schools by reputation. It might be a good idea to draw up a matrix with SU, BU and UDel in a row across the top and different categories in a column at the left (or right), such as climate, campus and local environment(urban/surburban/rural), first year tuition cost, whether or not there is a room and board contribution from the school, school size, battalion size, what the program looks like for your proposed major, etc., whether they have a top ranked basketball team (just kidding, though some people identify sports with school spirit). You can use this to compare the schools and what you like or dislike about them.
Remember that there is the possibility of transfer when the dust has settled. Perhaps someone else can comment on a strategy of accepting a scholarship to an expensive school with the goal of transferring it to a less costly one. Also, as others have discussed at length, you have to keep in mind the possibility that ROTC might not work out for you after you're in it, meaning that you would have to have a plan for paying for the more expensive school.