There are at least 5 vacation rentals I've seen within steps of Elizabeth House. Not all are lakefront, but they all seem to have lake views from their terraces. The "streets" leading up from the Lake here are really steps, so the houses get higher as they ascend from the lakefront thus the views don't get obscured.
The two kids I'm with - ages 10 and 12 - love the lake. They're in it every day. There's an abandoned castle above the town that you can explore on your own. The boys found old armour and weapons laying about and played knights. I climbed to the top of the tower and had a phenomenal view from the battlements. A falconer gives demonstrations most days (check the website for Castello di Vezio for times). A really nice but steep path leads back down to town. (We took a taxi up...too hot for the steep ascent today).
Varenna is the central ferry port to visit the towns in the mid-Lake area - Bellagio, Tremezzina (lovely Villa Carlotta), Menaggio, and Lenno/Villa Balbianello.
You can catch the train from Milano Centrale to Varenna, which I'd recommend because parking is scarce here. Private excursions, both auto and boat, are available in town.
The restaurants in this village are surprisingly good. Tonight my wife and I ate at La Vista, overseen by a world class chef, who imo could work anywhere in the world, but I understand why he'd choose Varenna. Dinner for two, three courses with wine, came to 115€. We were there for two and a half hours. Delightful.
Let me just say Varenna is a place, if you know what I mean. And it's contained enough to make your planning achievable. (Obviously, I love it. This is my third visit.)
Best of luck.