Just moved here – is the Eastside unsafe for girls?

I just moved to Houston and asked a few friends who live here where they recommend I live and all of them said stay clear of the east and live in Midtown/Montrose/Heights etc. I toured a few places and got a place slightly below highway 69 because I really liked the apartment (it's brand new), but my parents are super worried and want me to move to midtown/heights area. I'm in 77003 area, bordering downtown. Any perspective would be appreciated. Are they overreacting or is this justified and I should break my lease and look elsewhere? For context, the apartment is very secure and new – but we're worried about the surrounding area.