Varenna is a quite small village but is located in close to proximity to many places of interest. Nearby is Como a city definitely worth exploring. Also, being so close to the Swiss border, visitors can take advantage by going to Switzerland very easily.

Como is full of great shopping opportunities and more history. The town dates back to around 172 AD and is full of historical landmarks and monuments such as Medieval walls and towers and an intricate cathedral.  

One can take a train to Zurich from Como but the trip will last about four hours prompting many to want to stay over night in there. But there are closer cities and if one wakes up early enough Zurich can be a day trip and a great one at that. The Swiss charm is quite different from the Italian charm and of course is worth it to go and load up on incredible chocolate. Check out the Swiss Railway's website for information. One can also travel over the lake by ferry or boat, check out the Naviagazione Laghi for more information on this option.

Milan is extremely close, the fashion Mecca is loaded with incredible shopping opportunities, Italian landmarks, beautiful scenery, and a hot nightlife for which you may want to consider staying over.