What to do in Varenna for 1 day.

Buy Rick Steves Milan & The Italian Lakes or Rick Steves Italy 27th edition guidebook and take Rick’s Varenna self-guided town walk. Afterwards, take a 15m ferry from Varenna to Bellagio and walk around there too.

Taking a ferry and touring Villa Balbianello is a great experience. The gardens and location are beautiful, and several movies have scenes filmed there.
There's also a great uphill hike in Varenna yielding panoramic views.
Just taking the ferry and having lunch in Bellagio is a nice outing. The shops in Bellagio have more unique , higher quality gifts.
Wine tasting happy hour at the Hotel du Lac in Varenna is fun, with incredible lake views.Hotel du Lac is a wonderful place to stay. ( I'm unfamiliar with your hotel.)
Have a great trip.

We were in Varenna two weeks ago. The town is just so beautiful! I just looked up your hotel, it's located on the plaza. It has great reviews, but my suggestion is to actually stay in a property directly on the lake. Waking up to lake views, and sitting on a balcony watching the sunset is memorable. The lodging on the lake does require more steps when exploring, not sure if that's an issue.
Have a fantastic trip!

I would also suggest walking the grounds of the Villa Cipressi, a beautiful hotel on the hillside in town.

We stayed in Varenna last July for 5 days. If you only have one day I would ride the public ferry to the different towns. Then choose one to have lunch or dinner. The Villa Balbianello is beautiful to visit. You can visit it from the Lenno ferry stop. There is also a villa in Varenna known for its gardens.

Go to the gardens as suggested above. Shop in Varenna. Go to Hotel du lac patio for a glass (or a bottle) of wine and enjoy the views. I planned my entire trip to Lake Como (last time) around that patio.