Weekend visit — Downtown vs Galleria vs Museum District

Hubs and I are visiting to attend an event at the Children's Museum. We'll be renting a car for the weekend since we're also going to head into the suburbs to see friends for a dinner, but we would love to stay in an area where we'd have easy access to safe running paths (park or trail, ~8-9am in the morning…keeping in mind we don't run together and I run as a solo woman) as well as some decent coffee and cafe options. Never been to Houston so would love some guidance if anyone can weigh in on where to focus the hotel search!