I agree with Suki for Liguria - Noli is great!
Also Camogli - it's a beautiful small seaside village with excellent restaurants. There is a small Maritime Museum and a nice theater in Camogli - if there is a performance scheduled, you'll want to attend. One day, we hiked to the next village, Recco.
Both Noli and Camogli are smaller villages. We spent 3 nights in Noli and 4 nights in Camogli which was just about right. The rail station in Camogli is near the city center so it's convenient for day trips - we took day trips to Genoa, Santa Margherita Ligure and Portofino from there.
We did have a rental car but took public transportation for some of our day trips.
In Tuscany, Lucca and Siena are favorites - at the time we visited, Florence was super busy - it might be less so when you go.
With 45 to 60 days, you can plan for 4-5 days in several different destinations - as you do research, decide which towns/cities appeal to you the most depending on your interests. I'd suggest picking a couple of places to rent an apartment for a longer stay.
Edited to add: For our trip, we flew into Turin - it's not in Liguria but we thought that it was a good place to begin our trip - especially if you like cities as well as smaller villages. Our trip ended in Florence.