Sorrento Hotel in May

moderately priced

Meaning what , numerically? How many people?

I stayed here-- https://ilnido.it/ -- and would happily do so again.

The “city center” is on top of the coast. It’s not a large town. That’s why it’s so crowded.

I think you might mean on the hills above Sorrento or in the city center?

Sorrento is on top of a steep cliff, so there's not really a coast to stay on. We stayed here https://www.sersalesuites.it/ in April 2023 and we're extremely happy. It's about a 10-15 minute walk to the train station and about 5 minute walk to the ocean views.

If it's helpful, here's my Trip Report from our 2 weeks in Sorrento. https://community.ricksteves.com/travel-forum/trip-reports/trip-report-2-weeks-of-day-trips-from-sorrento

We stayed at Hotel Villa Di Sorrento in September 2023 and it was a great location. Easily walkable to the train station (which we did to go to Pompeii for a day trip and then to Rome). It is steps from the Piazza Tasso. The breakfast was included but wasn't great, but there were other places to go if you wanted something different. It was probably the least fancy hotel we stayed at during our trip but no real complaints about it. I'd stay there again.

As others have intimated, the "city center" is about a 3 minute walk to the "coast". I liked being right in Sorrento for the vibe and the convenience but there are lots of options in the hillside behind Sorrento and in the areas along the coast.

It's hard to know what kind of vibe you're shooting for. Booking.com or similar is gonna be your best bet to personalize your search

It is already late to book Sorrento for May, so don’t put this off. We had to take our 6th choice, but we were very happy with the large, cliffside, Ambasciatori. Paid extra for balcony and Vesuvius view. Some ferry horn noise. Nice cold air conditioning.

Rick called it “a worthwhile splurge”, but it is probably too expensive, as far as I can tell from your cryptic requirements.

We did not go to this area until our fifth trip to Italy.

We stayed here last fall-our 2nd visit to Sorrento
( splurged on first so don’t think that hotel fits your budget)
Very comfortable, great location, no bkft but several nearby cafes/bakeries, had a peek of the sea view from balcony, manager was so nice and helpful

https://www.diamondsuite.it/

Agree with Tim -at this late date you’ll need to book soon
Check booking.com for availability-use the filters fir budget, location , etc

Search from last 2 years might have something
https://search.ricksteves.com/?button=&date_range=2y&filter=Travel+Forum&query=Sorrento+hotels+

il Nido (ilnido.it) is above the town but they have a very good shuttle that makes day and night trips easy. The hotel is comfortable, with a spectacular view. The restaurant serves a wonderful breakfast buffet but they really shine when it comes to dinner! It's been my favorite place for dinner (on the balcony overlooking the Bay of Naples) for 12 annual visits. Sunset is magical - a necklace of diamonds appear around the Bay.