My personal preferred way to explore a new city is to take a hop-on-hop-off bus tour the first day. If you have a 48-hour ticket, you can ride around once to get an overview, then ride again with stop-overs at the places you found interesting.
Another idea, particularly if you want to meet some locals, is to check Eventbrite and Meetup for the city you plan to visit. I’ve found a multitude of happenings that way, mostly free.
Regular hiking is good for the body and the mind. Several Meetup groups have regular hikes in the Austin area, as does the Sierra Club and others.
I have regularly hiked with the Monday-Friday Hikers for 7+ years. Most of us in the group do not work a regular 9-to-5 job, so our hikes begin at 9:30 AM. We usually walk for 1 to 3 hours.
We do not recruit new members directly. Instead, we encourage people to take the “Hiking Austin Trails” course given by Austin’s Lifetime Learning Institute. Tuition for that course is just $20, and it meets 8 times for hikes on some of the same trails that the Mon-Fri Hikers frequent. Anyone who is comfortable with the Hiking Austin Trails hikes is welcome to join us.