Easiest way to travel from Avignon to Monterosso?

I don't know about this, I'm afraid, but this section of the board is for reviews of hotels, restaurants and attractions. You'll get more answers if you post in the main France or Italy boards.

It's going to be a slog with a few changes. I've never been to CT, so can mainly give you the French side of the trip. You need to take the train to Marseille, either the airport for a flight to Pisa, or take the train across to Genoa and beyond. Now someone else can give you the rest of the trip. Check rome2rio.com for info.

Train would probably be the best way to go but either way I would make a reservation with what ever hotel you choose as soon as possible because it is not uncommon for the hotel's to be booked far in advance ( like 6 months to year). My favorite hotel is Porto Roco, the view is amazing!

The best train connections from Avignon Centre to Monterosso take 10 hours, for instance departing about 9:15 a.m. with 3 connections or 13:40 with 2 connections (arriving at midnight). Some people would break the trip with a stay in Nice, but I would only do that if you have time to stay in Nice for a couple of nights to see it.

www.skyscanner.com is a good search engine for flights from Marseille to Pisa. If you fly, then the trains on either end of the trip can be as fast as an hour each, but it does depend on the time of day, and that doesn't count connections from the city centers to the airports. How to Look Up Train Schedules and Routes Online gives you the DB train schedule link and tips for using it.

We did this trip a few years ago, but did exactly what Laura recommended & stayed in Nice before taking train to Monterosso via Genova.
It was a very long train ride ( 5.5 - 6hrs)
We stayed at Hotel Baia in Monterosso. The hotel is conveniently located near the train station & on the waterfront.