Looking for advice on staying in Northern Italy (Milan area - 2 weeks) and going out to visit Cinque Terre, Florence, etc...would like to avoid renting a car and travel by train/bus. Thinking we could rent a villa or apartment within walking distance of transportation. Planning on April of 2019.
Thanks!

We visited north Italy, albeit in summer, mixing some very busy and some quieter locations, by bus and train. My report and photos here, if you're interested

Northern Italy and a bit of Bavaria, a family trip

We did not base in one place, however, which sounds like your plan. (We stayed in Milan, Vernazza, Volterra, Florence, Verona, Trento, Ortisei)

In recent years I've done a number of trips where I based in Milan and did day trips. I've done Bergamo, Lake Como, Lugano (Switzerland), Pavia, Parma, Genoa, Cremona (not all on the same trip). I didn't do it as a day trip but Turin would also work well. All by train. The hotel I really like, Hotel Berna, is a five minute walk from Milano Centrale which has great connections to all parts of Italy. It's also only a quick metro ride from the center of Milan (or walkable in about 25 minutes).

But if you are also interested in Florence, CT, etc. it might make more sense to have two bases, use Florence for the more central parts. There are lots of good day trip options there (in some cases buses make more sense in that region). Or have a base in somewhere like Verona for that region (day trip options including Lake Garda, Vicenza, Padua, Mantua, Treviso, Ferrera. Still another option would be Bolgona with day trips to Modena, Ravenna, Ferrera. I've done all of the above. Never had a car for any of those places.

I would look at a map of Northern Italy and plot out towns that interest you, then go to trenitalia (train) site and research train trip times. I usually keep it to under two hours each way for a day trip (closer to an hour is better). You'll also see which ones are easiest (have more departure times, etc.). In many cases there will be departures from Milano Centrale hourly to a lot of those towns meaning you don't have do as much planning in terms of what time you need to get there and get back. But a little research will go a long way.

Here's the trip report from my most recent trip that I based (5 days) in Milano and did day trips. Italy thru new eyes / Chasing the sun in March

Don't need to rent a car for places you seem to be interested in - you are planning to base in one place the whole two weeks? I'd consider moving around and staying several days in each place to be better able to expand your horizons. anyway for lots of info on Italian trains check www.trenitalia.com; www.seat61.com; BETS-European Rail Experts and www.ricksteves.com.

Thanks! Will consult a map and figure more closely what we want to see and go from there....good advice!

As PQ says, start with a train map, read the seat website then use something like rome2rio to look at a few option (nb data is not perfect but gives you a starter for 10)

Bologna is a wonderful city... about 1.5 hours by train. But also could stay there (as someone else suggested) and visit the wonderful towns close by. It's nice to stay put... but also don't want to spend a third of every day on a train.