Cabs are a fortune. The college, in Harvard Square, is closer to MGH. You can actually use the red line (T) to get from Harvard Square to Charles/MGH (~3 stops) which is easy, direct and will only cost $1 per trip. The MGH stop is a short walk to the main entrance. You can also take the red line from Harvard Square to Park Street transfer to the green line (the E train) to get to Brigham (Brigham Circle stop).
There is also a shuttle (M2) from Harvard square to Harvard Med Scholl (right near Brigham) but without a student ID you need a ticket which your friend may be able to help you get.
I'd splurge on the hotel just because it would end up being more comfortable and convenient. I don't remember what their rate was, I think its $150/night.
By the way, I made a mistake earlier. It is not a Holiday Inn on Longwood, it is a Best Western. There is a Holiday Inn near MGH. I mixed them up.