La Spezia, Levanto, or one of the Cinque Terre towns?

I've stayed in Levanto twice and would stay there again. It's a nice town in itself, even if not quite the quaint "town built into the side of the hill" that is true of the five villages. Levanto is just one train stop north of Monterosso and is part of the park and included in the train pass. La Spezia is included in the train pass too. But I have not actually been there except to change trains. I've heard a few positive comments about La Spezia but mostly negative.

There is excellent train service between all the CT towns plus Levanto and La Spezia, even fairly late I think now. So you could have dinner in any of the towns and take the last train back to Levanto or something. A quick check of train schedules shows trains from say Vernazza to Levanto at 22:15, 23:28, and 00:17, if you really want to be out late.

We stayed in Monterosso, but our tour group went to Levanto for dinner one evening at Zita. It's a simple restaurant with great atmosphere, on top of the incredible valley. It was our favorite meal in the region. The Tiramisu was the best we had in Italy. Family run restaurant. Recommended by our guides aunt who lives in the village. Wonderful experience. www.zitalevanto.com

Monterosso also meets all 3 of your criteria.

La Spezia is an ugly port city. Ditch it.
In the Cinque Terre the town of Monterosso meets all you requirements.
If accommodations are not available for you dates then consider either Levanto or Bonassola, however in May you shouldn’t have big problems finding accommodations in Monterosso. Just don’t wait to the last minute. Levanto and Bonassola will definitely have vacancies in May.

I agree with the others in that Monterosso would be a great choice as it seems to tick all the boxes. A few thoughts.....

1. Monterosso has the best beaches of the five towns and there are two different parts to it, one in the old town and one in the new town. Part of the beach areas have free access, and for others there's a small charge. Those with the beach chairs will have a cost. Roberto or one of the others can provide more information on how to find the free areas. The beach isn't completely sandy but I don't recall it being too rocky. The beach in the old town is smaller.
2. There are lots of restaurants in both parts of town. One of the big favourites with many here is Cantina di Miky (has a compact but nice patio overlooking the ocean), which is in the new town not far from the rail station. I also like Ristorante Belvedere in the old town.
3. Monterosso tends to be quite vibrant in the evenings as the restaurants are open and happy travellers are wandering about and having a few drinks in the local bars. As I recall, Cantina di Miky also offers a good selection of craft beers.

Monterosso is also a good "home base" location to catch the Ferries.

It's a very good idea to book as early as possible. If you can't get a room in Monterosso, Levanto is a good second choice. The beach in Levanto is also good and very large.

Another vote for Monterosso. We stayed in the "old town" and really enjoyed it in the evening. Beach in the "new" part tics off the "beach".

Roberto and Ken will always give you good and reliable information.

We didn't need a car, nor did we want one.

Regarding beaches.
Portions of public beaches in Italy are given to beach establishments under a concession agreement. These establishments are called “Stabilimenti balneari” in technical terms, but are known in everyday language as BAGNO (plural BAGNI) or LIDO (plural Lidi). So one such establishment might be called “BAGNO ROBERTO”, or BAGNO BLU, or LIDO ANYNAME. Each regional government regulates concessions differently. All require that some portions of the beaches to be left free of concessions. For example a region might say that every 200 mts given in concession there must be 100mt left free.
The first 5 mts from the water is state public property that must be left free and unencubered. You can walk and sit there but nobody can plant an umbrella with chairs on the first 5 meters from the water edge..
If you go to the satellite image on Google Maps you can see the portions of the beach given to a concession because it will have a few rows of nicely lined umbrella. The portions where you just see scattered people but not nicely lined umbrellas, are the free portions.
I doubt that in May many concession establishments are up and running. They usually start operating in June, but if the weather is good and the place is busy, maybe some will start working in late May. If they are, tha is where you can rent your chairs, your umbrella, and even a changing cabin. Italians rent a changing cabin because they rent by the week or by the month and use the changing cabins as a storage for beach stuff (when I was a kid I stored so many toys inside our cabin, my mother couldn’t even get in to change her clothes). If you just go there for a day and have no kids’ toys to store, don’t waste money renting a cabin. You can change your costume in the bathroom or on the beach using a towel around you

I have visited some beaches in Europe when we lived in Germany 25-30 years ago and never found any of the beaches that wonderful, except on the Greek Islands. Even the South of France, the beaches were a bit nasty, with refuse washing up. Nothing compared to the Caribbean or even Florida. Still, some of the cities near or on beaches are wonderful.

Are you going to site see or just relax and go to the beach?

La Spezia is a pleasant, friendly city that has improved considerably in the last decade. It is active but has few tourist or historic attractions. It has no beach, just a pleasant promenade along the sea. I think Levanto is the better choice.

I would go for Monterosso because any other place, including Levanto, is not going to have much life in May.

What months are you typically able to rent chairs? We will be in Monterosso in mid-October. While its doubtful I would go swimming, I sure would love to sit in a chair for a few hours and just enjoy the view and the sun!

Do not stay in La Spezia unless you want a second rated town with a cruise ship problem. Stay in one of the five towns, cinque terre. My favorites are Manarola or Vernazza, but maybe they are too small for you. Monterosso, like mentioned by others, might fit the bill.

https://www.lecinqueterre.org/bagni/bagnimonte.php

Above is the list of beach concession establishments in Monterosso. I am sure all are open June through September. However given the fact the Cinque Terre are so popular year round, it is likely that the establishments there stay open longer, as early as end of April or early May till the end of October. Give them a call (not now in winter of course) and they let you know their opening dates.

We stayed in Vernazza, which is wonderful but not what you are looking for. We did a day trip North of CT and found the following. I think Levanto might be a good choice. It is a surfer beach, so you get a cool surfer vibe. Big enough to have a number of bars, restaurants and a few surf shops and scuba shops. Bonnasolla is 1 town North, and is also cute. There is a pedestrian walkway with a long tunnel connecting the 2 towns. Moneglia is much smaller and to the North, but has a nice little beach. All have easy access to the train line into CT.

I would highly recommend Levanto. First town north or Cingue Terre and train line right there. We stayed there and I it was beautiful. Maybe better rates than Cinque Terre itself. We only walked one of the trails but saw all he towns easily in a day and a half. We drove to Levanto but once there parked and just took he train and walked. But just be prepared to wait for trains there really isn't much of a real schedule.

Tom, I take it you last visited the Cinque Terre some years ago? Trenitalia has added much more train service through the region in the last few years e.g. the "Cinque Terre Express." I first visited in 2007, but when I visited again in 2017, I was surprised how much more frequent train service had become. Badly needed! And yes, they do keep to a schedule, even if trains in the riviera are subject to delays.

Thanks all. Monterosso is the winner. Just booked a spot there and BONUS they are having a lemon festival while we are there.