On the mountain above the town, there is a Villa Serbelloni, owned by the Rockefeller Foundation. The villa itself cannot be visited, but the park (Parco di Villa Serbelloni) can, though only with a guide.
There were originally two luxury hotels in Bellagio: the Hotel Gran Bretagne and the Grand Hotel Villa Serbelloni. The first one is now in ruins and awaiting reconstruction.
And the second one works, the most famous people of the world stayed there: Winston Churchill, Presidents Roosevelt and Kennedy, the Rothschilds, Clark Gable and Al Pacino. George Lucas lived there during the filming of the most famous movie of Lake Como - the second part of Star Wars - Attack of the Clones.
Prices at the hotel start at 700 euros per night, but there's a lifehack. The Residence L'Ulivo (booking.com) offers nice apartments and located on the territory of the hotel. Prices are also high, like everywhere in Bellagio, but they are several times lower than the prices of the Grand Hotel Villa Serbelloni.
There is excellent parking, a terrace and cleanliness of a five-star hotel. It has all the amenities of the main hotel, you can walk around the area, swim in the pool or have breakfast in the restaurant. We stayed here for 4 nights, were very satisfied with this villa and can recommend it, especially if you are traveling by car.
Few times we visited indoor pool with a child, it is very suitable for small children. The only pity is that you have to walk a few hundred meters through the park.
The hotel has its own small park and promenade.
Bellagio is very beautiful, especially in the evening.
Behind the old town is a beautiful waterfront park.
The final point of the walk is Villa Melzi (https://giardinidivillamelzi.it/en/home-eng/info-eng/), the classicist country residence of the Duke of Lodi, built in 1808-10. The villa is situated on the shore of a lake and is surrounded by a beautiful park.
Although not many tourists come here by car, it is possible. What's more, Bellagio has a pier from which car ferries and passenger boats depart regularly for other places on the lake. You can find the schedule here https://www.navigazionelaghi.it/.
Though you cannot enter the town by car if you do not have a hotel here. And if you have don't forget to ask the hotel reception to register your car online.
From our villa we also went to the very edge of the cape, Punta Spartivento, where there is a restaurant and a small park.
And, of course, we walked around Bellagio. The streets are beautiful, but not as interesting as the promenade.
On the mountain above the city there is the belvedere Macalle, which offers a magnificent view of Bellagio and Lake Como.
Viewpoint can be reached by foot, download the maps.me app. But you can also go by car, the road is quite narrow and there is a small parking lot for 1-2 cars (45.963035, 9.256965).
Getting there: the main route from Milan is by train to Como and then by ferry or bus C30 (https://www.asfautolinee.it/it/linee-e-orari-in-pdf). An alternative route from Milan is the train to Varenna-Essino, then 15 minutes by ferry to Bellagio.