Cheap overnight parking around the Galleria?

I'm headed to Houston, staying at hotel in the Galleria area. Anyone have any recommendations for parking? A quick search in this sub showed me that parking can be difficult, but I didn't see anything specifically about overnight parking. The hotel charges a valet + daily fee, and I was wondering if there are other cheaper options. Thanks!

edit: Thanks for the helpful replies, looking forward to visiting your city soon!