First, TripAdvisor lists this as "Hostel Piran" but it is not a hostel. It is the Hotel Piran. There is a youth hostel a bit further inland.
Anywho, on our first visit to Slovenia, my partner and I stayed here towards the end of April and were pleasantly surprised by the size of our suite. Separate living area with adjacent toilet/sink and two sinks w/shower adjacent to the bedroom (w/bidet - strangely not with the toilet).
Large walk-in closet/changing area and spacious patio which overlooks the beautiful harbor and walkway that winds its way around the docks and so forth - nice for people watching.
The hotel is older, the king bed was, as we've become accustomed to in Europe, two twins/full size beds pushed together and covered with king linens (don't fall into the crack!). The furnishings were, again, older but everything was kept clean and neat.
The staff are multilingual, and very friendly and helpful about anything you may need. Right across the road is a tourist bureau wth an equally helpful gentleman.
The rooms include a nice breakfast with hot and cold items, and some typical european fare. The auto coffee machines really didn't put out what we'd term typical capuccino or espresso drinks. But the great thing about breakfast is where it's served: truly a panoramic view of the Adriatic sea which was spectacular.
wi-fi is available in the hotel for 2.50 euro/30 minutes (to be used at one sitting). It's reliability was a bit spotty. Some of the casual bars along the waterfront give you 30 minutes free on their computer (or wi-fi to your laptop) with any purchase. I found a nonsecured wi-fi connection near "Bar Aroma" in the square that required no credentials and was high speed.
Realize that if you plan on taking public transport from Italy, boat service to and from Venice is seasonal and usually from a nearby town. Bus service to/from Trieste, Italy is ONLY weekdays (though frequent). If you need a taxi to Trieste Rail station it'll be 49 euro and to the airport 89 euro, so plan accordingly (bus was only 5.40 euro).
Quick note about Piran - don't expect any fancy shopping or boutique stores - this is old country charm at its best and there is some reasonably good food to be had. If there's a festival in the main square GO TO IT! It was the highlight of our trip with a arts/crafts/fleamarket going on and live entertainment that ran the gamut (marching bands, singers, classical bands, etc) - lots of fun. Beer/snacks/coffee are served at a variety of little restaurant/bars in the square.
And a little hiking up and around the narrow streets wil reward you with breath taking views of the surrounds. We even stumbled onto a hidden rocky beach with someone nude sunbathing with his friends/family. This was off the beaten path a bit, but doable with the right shoes and strength.
