Monterosso

What time of year? In my opinion, Monterosso is would not be a high priority for a day trip from Genoa - it's not especially picturesque and is likely to be crowded. Have a look a Camogli or Santa Margarita Ligure or Chiavari.

Judy, what time of year are you planning to travel? A day trip to the Cinque Terre is very possible from Genoa - although it might take just a bit longer than an hour - but the region may not be the best to visit during the colder months.

If you're NOT traveling in colder months, I'd encourage you to see more of the area than just Monterosso. While the largest of the villages, there's not enough there to fill a day, IMHO, and every one of the villages have a bit different scenery and so are fun to explore...which is what you'll largely be doing, on foot, if not going for hiking the trails. You can take the local trains between the 5 (they only take a few minutes from station to station) and there is also ferry service during the warmer months. They're short on things like museums and other indoor activities - although they all have churches that are interesting to visit - so you'd want to leave some flexibility in your schedule so you can choose a sunny - or at least dry - day to spend outside.

Do expect them to be very busy during high season.

I plan to go next summer.

Mikes' suggestion is worth considering. It would be closer, and I'd guess that it would be less busy other than the beach, if it's hot.