This may not be fair for me to offer an answer because I spent 2 nights in Varenna and about 2 hours in Bellagio, and did not venture into any of its residential areas. My memory of our brief stop in Bellagio was the row of touristy shop windows with glittery jewelry and Murano glass. After one overpriced drink at an outdoor harborside cafe, I was ready to get back on the boat and return to Varenna.
Varenna had more the feel of a town where ordinary Italians actually live. The few streets are mostly steep pedestrian alleys with broad shallow steps, and everywhere's a hike, but a scenic one. In the afternoon the school kids commandeer the main piazza for a soccer field. We liked the Hotel du Lac where the water lapped right below our tiny balcony, and we had a memorable seafood and pasta dinner at Osteria Quatro Pass. That said, Varenna's hardly a hotbed of entertainment, so I'm not sure if it will pass your boredom test. Lake Como in general seemed pretty mellow.
Our favorite day trip was to Villa del Balbianella on the island of Lenno. The house and gardens now belong to the Italian Trust, and the collection of artifacts are better than many museum's.