Hotel area recommendations?

Me (27 F) and my best friend (28 M) are visiting Texas for the first time just after Christmas and we’re super excited! We’ll be there for a wedding in League City but decided we want to stay in Houston to have a fun Texas experience. We’re super excited to try authentic southern BBQ, check out some bars, and see some live music. I’m also hoping to visit the Space Centre and Museum of Natural History. Any suggestions on neighborhoods to stay in (or better yet, hotel recommendations)? We’ll be in 1 room with 2 beds, both of us are queer so not each others type haha. The cheaper the better but up to 300 a night is doable. TIA!