LOTS of schools cover room and board if you're on an Army scholarship. There's a list of them on the sticky "Room and Board" at the top of this forum.
I wouldn't necessarily use that post - it dates past several years ago, a lot has changed. I know that there are some schools that no longer offer free R&B any more. It's best for the OP to ask admissions themself.
Also OP - just because it is transferable DOESN'T mean that it will be transferable. It's not really that easy to just pick up a scholarship and move it elsewhere. You see, you have to consider both the losing Battalion and the gaining Battalion. And, if the gaining Battalion is in a different Brigade (geographic region) than the losing Brigade, things get even trickier.
I think I remember from last year's graduating class ... it was Clarkson (I think, not 100% sure) that said originally all transfer requests were denied, but then CC realized that a decent chunk of the scholarship winners were awarded schools, that for one reason or another, didn't/couldn't attend, and CC ultimately approved transfers.
And with the way budgets are being cut, who knows how much CC has. So, just be aware of placing your money on transfers.
Also - some schools have crosstown agreements with other schools; in other words some schools serve as a host battalion for another school. In Drexel's case, it is a crosstown school ... for St. Joe's I think. This may not be a big of an issue since they are fairly close to one another, but in other schools - distances may be a factor. IE: Getting up 1 hour earlier than everyone else to avoid traffic and make it to the host school for PT in the morning, and then doing the same for class/Lab etc.