$700 per night is a lot. Are you planning to rent one separate hotel room per person?
I think in your case it might be beneficial to rent a house/apartment through AirBnB or VRBO.
I presume you plan to travel by train. I would also suggest STRESA for lake Maggiore, MONTEROSSO for Cinque Terre, VARENNA for lake Como. All are served by rail. For lake Como, also check Bellagio and Menaggio. They are not served by rail (Varenna is), but they are a very short ferry ride from Varenna and, being a bit bigger, may offer more accommodations. Bellano, the next train stop north of Varenna is another choice, although ferries to Bellano are less frequent than the other 3 towns (but it’s just one train stop from Varenna, so you can easily go there by train).
For the Cinque Terre, I suggested Monterosso because it’s a bit bigger and has more accommodations than the other towns, also more trains stop there (including high speed Intercity trains), however any of the 5 towns would work.