We were thrilled with our visit and only wish we'd booked a longer stay. Varenna is a beautiful little village with delicious food, historic castle remains, and fantastic hiking opportunities. The apartment was perfect with plenty of space for our family of 5 (all 3 children are young adults now). We had room to play games and relax and plenty of sleeping space. Our room had a divine view of the lake and mountains, which we greatly enjoyed morning and night. In the evenings, we could open the windows and catch a jazz band that was playing in the square and we awoke each morning to the birds singing and the old church bell in the square.
Practical matters: We appreciated the hairdryer, the dishwasher, the excellent bathroom and the fans. My kids note that the wifi worked great downstairs, but was weak upstairs. There's no elevator, which we didn't mind, but since you'll need to walk up a few flights of stairs, it may not be right for everyone. Also you should buy groceries before you arrive, because although there's a little bodega across the alley, its offerings are very limited (and cash only) and the closest supermarket is in the next town. A great variety of tasty restaurants within walking distance though, so you can always eat out.
We drove from Switzerland, and found free parking nearby (we left the car parked there for our whole stay).
Recommend walking to the Fiummelatte (one of the world's shortest rivers), the Baluardo, and the castle. The gardens were also quite lovely in June. Great jumping off point for taking the ferry to Bellagio or other nearby towns.