Hello!
I had exactly the same problem, as I wanted to choose among these 3 options. After careful consideration, online searching, lots of emails and phone calls, I finally booked a studio in Gateway Apartments.
The rooms are very nice, bright with large windows and the location is perfect too. Elm Row may be busy generally, but if you look at the map, the apartments are situated in a block at Montgomery street, where you can definitely avoid the noice and the traffic. Thus, you can combine silence for studying and walks-socializing at Leith Walk and the bars around.
Sugarhouse does have a better location, in the historic part of the city, but in my opinion, when you live in a city (not visiting it as a tourist) you enjoy more the local bars/restaurants/shops/amenities than the walks in the historic center. Visiting the Castle and the souvenir shops can be boring!