One of your first stops should be Galena Creek Park. Here, you'll be able to find your bearings and pick up some great ideas before you set out exploring.
When it comes to things to do in Reno, Galena Creek Park is recommended by fellow travelers. And in great news for your budget, admission is free. Mt. Rose Ski Tahoe, Bowers Mansion and ArrowCreek Golf Course will round out your day and are not far from the tourist information center.