Visitor curious about safety in Galleria area

We will be visiting Houston in a few weeks for both business and vacation. We chose to stay at the JW Marriott Galleria as it appeared to be fairly centrally located and near some nice restaurants. However, when my BIL found out we were staying there, he sort of freaked out and said it was “in a very dangerous part of the city”. He said we should stay in either downtown or near League City where he is. Unfortunately we booked a non refundable rate on our hotel. Is it really something we should be concerned about? My BIL is prone to making hyperbolic statements so I would just like to get the opinions of other Houston residents. Thank you!