If you don't live permanently, Jinjiang Inn near the gate and 7 days near the back door are all good.
The other one on the first floor didn't lie to you. Beijing Foreign Studies University has no special study room. If you need self-study, the East Campus is basically in Yifu Building (with air conditioning, the 4th to 6th floors are generally quiet and sparsely populated) or the canteen (don't worry about coming to class suddenly, but the food is noisy). Non-foreign students in these two places can also enter, and the library is always crowded and needs to swipe their cards to enter. For the west campus, you don't need to swipe your card to enter the China Business Building and the German Building, but you can study by yourself.