Positano

Here are a few:

https://www.covodeisaraceni.it/

http://www.hotelposeidonpositano.it/

https://sirenuse.it/en

http://www.villafrancahotel.it/en/

You may want to start saving your Euros right away.

Thanks... wow on euros!

We were in Positano several years ago and stayed at the lovely Hotel Savoia.
Wonderful accommodation with Panoramic Views. Great location above the square. Easy access to seafront promenade and beach in less than 5 minutes.

The most fantastic way to get there is to take the fast train from Rome to Salerno. Once there, walk down to ferry and take that to Positano. To see the Amalfi Coast from the sea is magnificent.

http://www.travelmar.it/en/

I just bought our tickets when we got there, but here’s the schedule. I decided to wait because if it’s bad weather, they won’t run. In that case you’ll have to take the bus. I made sure to do my research and find out which bus, etc. before our trip just in case.

More than one ferry company serves Salerno> Positano so explore options here:

http://www.positano.com/en/ferry-schedule?from=salerno&to=positano

I'd also recommend Hotel Savoie as it's very comfortable and not far from the beach. Be sure to specify view rooms on the front (although cost will likely be slightly higher).

Positano is not as easy for transportation, as there's no rail link. The easiest and most comfortable method would be to take the high speed Freccia or Italo trains from Roma Termini to Napoli Centrale. If your budget will allow, use a private car service from there to Positano. This is one option to consider - http://www.monettitaxi17.it/English.htm . Be sure to arrange the return trip as well.

Another option would be to either take the Circumvesuviana or Campania Express from Naples to Sorrento, and then a Taxi to Positano. You could also use the Ferries but if the weather is less-than-perfect, it may not be the most comfortable trip.