Scared cat: keep close or let her be by herself?

3 months ago, I adopted a cat. From the start she has been very scared and is mainly hiding when I'm home. She found a secure spot under the TV and seemed to slowly open up and be more comfortable around me, especially if food is involved. At first I kept her in the living room, but 2 weeks ago I let here go around the house and left the door always open, because she seemed eager to explore. Since a week however, she seems to spend most time on the upper stairs, as far a way as possible. I understand that she wants her own space and I definitely want to give her all the time she needs to be more comfortable around, but I'm wondering if it was the wrong decision to let her out of the living room. On the one hand I want her to be at ease, but on the other hand I don't want to her to be scared of my for too long because we never interact this way. Would it be better to keep her in the living room again, or should I be more patient?