There are several golf courses in Napa. The closest to the Vino Bello is the Kennedy Park golf course.
Hiking in Napa is available at the following parks:
Skyline (the closest to your resort)
Bothe: Located near Calistoga, has great views and you can see redwoods
Jack London Park: Some great hikes, you can also see a museum dedicated to Jack London, and the remains of his estate
There is a hike behind the winery Bartholomew Park that goes through mixed madrone and pine forests as well as redwoods
Stuff to do in Napa besides drink wine:
Bale Grist Mill
Walk around any of the historic downtowns
As someone mentioned above, the Uptown and the Opera House are both concert venues. Silos and Jarvis Conservatory also sometimes offer shows.
The Oxbow Market
There's a lot to do in Napa besides just wine! You could also take day trips to the coast, to parks to go hiking in Northern Sonoma (Annadel, Sugarloaf...), the Russian River (if you will be here when it's warm), San Francisco...