If you want to add a little more culture to your getaway, put Municipal Museum of Postal Services on your itinerary. Check if there are any guided tours or simply roam around at your leisure.
When you've spent a bit of time at this museum in Penza, why not make your way to Penza Zoo, Penza Regional Museum, and Penza State University? They're near Municipal Museum of Postal Services and also popular with many tourists.