The basement is definitely the one place where Luna can safely be herself. Because their parents allow them this space, Luna can let loose and be more comfortable after an entire day of rigidly conforming to everyone's expectations that he be a boy:
The parental units pretty much designated the basement as our private space. We had our bedrooms and shared bathroom down there, plus the big room where we could hang out and watch TV. Mom and Dad rarely ventured downstairs, and when they did they always announced themselves. (5.4)
For Luna the basement represents a place where she can safely be herself without fears of repercussions. Of course, the basement is also a place where no one else is around, so she's not really challenging societal norms when she hangs out as Luna. In this way, we can understand the basement as representing both freedom and isolation. Luna both expresses herself and hides from the world here, and to really live as Luna she will eventually have to leave the basement and venture into the real world.
We've got more to say about the basement, so be sure to check out the "Settings" section.