Varenna is very small, and is best enjoyed on foot.
The biggest draw of Varenna is simply to be able to stroll around by the lakeside or through the winding alleyways, enjoy the traditional Italian architecture and take in the serene atmosphere.
The castle of Vezio whence you can admire a beautiful panorama of Lake Como. Also, you can meet the Falconer of the castle, showing birds of prey to tourists.  Note that the castle appears to be closed in winter, only open between March-October.
The fiumelatte is a waterfall that runs through the village of the same name, a 15 minute walk from Varenna. This is along the main road south of Varenna, although a more scenic walk to the head of the waterfall is available by taking the road up past the exhibition centre, above the main highway.
There is a motor boat hire business operating in front of Bar Il Molo on the lakeside, providing the perfect opportunity to see Varenna and the other villages from the lake.
Artist Roberto Butta is a local painter who produces oil on canvas paintings and whose gallery is open in Varenna April to September.
There are also a few boutique clothes, art and gift shops.
The Marcelleria Salumeria, LIllea PIetro Matteo just off the main square, sells good quality local cheese, meats and wines, along with fresh bread and other groceries. It closes after the morning rush until 4pm.
There are two competing gelataria are next to one another on the lake front.
For finer dining, the lakefront restaurant Vecchia Varenna, offers a range of local fresh dishes on a regularly changing menu.
There are a few bars around, specially on the lakeside. L'Orso is last one to close (at 2 am).
A good breakfast is available.