Lake Como - hotels and itinerary around Bellagio / Varenna / Menaggio

How soon is this trip?
Accommodations in the area are limited and book up very early

I would start looking on booking.com now to see what is available

There's not much budget- friendly lodging in Lake Como. I would watch some u-tube videos on the three areas, and see what appeals to you. Expect large crowds from April thru October. Do some Searches here, as this is a frequent topic. Search on booking.com for accommodations, and read the reviews, which are pretty accurate. Then, book direct for the best prices.
You omit important details, like group size, age, mobility. There are lots of steps , and many hotels don't have lifts.
Have a great trip.

All 3 towns are quaint.
Varenna is very small, and since the train stops there, it fills quickly. So prices are high.
Bellagio, across the lake from Varenna (10 min by ferry) is slightly larger, but being the most famous town on lake Como, it is also crowded and expensive.
Menaggio is the largest (not by much) but it gets crowded as well in summer, and I don't know when you are going. In my experience it is a bit less expensive, but nowadays not much is available under $200/$300 a night on Lake Como.

We are looking for two nights accommodation - aiming for authentic, charming and lower end budget wise
All info about Bellagio / Varenna / Menaggio would be much appreciated

I think Residence La Limonera in Bellagio may work for you.

https://www.booking.com/Share-RcUdWA

Don't dismiss Bellano, as possible destination. It doesn't have the frequency of ferries as the famous 3 towns you mentioned, but it is a short train ride to Varenna (it's the next train stop going north).

Check out Hotel Beretta in Varenna. It's close to the train station and ferry dock. We liked it and would stay there again.