We will be in the Cinque Terre for 5 days in July and were thinking about taking a day trip one of those days. The question is...where??? We will be using public transportation, want to go inland as opposed to up or down the coast, and would prefer to be on the bus/train for no longer than 1.5 hrs each way. Do you know any memorable places that meet that criteria?
1.5 hours could get you to Pisa although there is really nothing there but the leaning tower and some adjacent historical grounds. Not a bad day trip if the leaning tower appeals to you. 2.5 hours will get you to Florence.
After reading Jennifer's comment, I suggest that she has the best idea. You can take a round trip ferry ride from Monterosso to Portovenere. The fare is about 13.50Euro. If seas aren't too rough, the ferry pulls into the towns. Have lunch in Portovenere and come back. It's very relaxing and super scenic. We did this on our most recent visit. BTW, Portovernere seems to get left out of the Cinque Terre stuff. It looks just like the 5 towns. Nice places for lunch.
IMO, Lucca would be a good choice, but it will be closer to 2 hours.
I would still stay in Liguria, and arrange a side trip to Portofino, Portovenere, Santa Margherita Ligure and Genova. These areas are fantastic and absolutely beautiful! There are so many options for you in this beautiful region..from olive oil tastings, Pesto tastings, Wine tastings, Schiaciatta & Farinatta tastings, Palazzo visits, Aquarium visit in Genova, Castle visits, beautiful churches to see, small ferry/yacht day cruises, etc, etc...
Ofcourse, you can always go to Tuscany for the day, ie: Lucca, which is a walled medeival city, absolutely beautiful...rent a bicycle when you arrive and enjoy!
Just to elaborate. The towns are reached by a local train route that goes North/South(ish). To go inland, you first have to get to a transportation hub on either end of CT and make a connection. That's why what you are asking is impractical. The local trains take longer that the faster intercity trains and connections add to your travel time.
Next time I'm taking Jennifer's advice. That sounds ideal.