Framura

buy my shuttle bus tickets at the station (which are cheaper than on the bus) to take it to Costa.
There are not very many restaurants or markets open during off season, but the accommodation has a full kitchen so if you bring groceries ( you can get some things at a local market/bakery close, but be mindful they close down mid day)
 the hostel is approx 30-40 minute (depending upon one's fitness) climb from the railway station. 
Kitchen is well stocked so did not feel the need to visit nearby restaurants .
Please be sure to arrive at the train station before 9pm otherwise there’s no shuttles and would be nearly impossible to climb the stairs in the dark all the way to the top. But otherwise she was kind enough to pick me up and I voluntarily gave her €5.
Be prepared to walk up the hill if you miss the last bus from Framura to Costa. The closest supermarket is in the next town down hill. In Costa there are two nice litlle restaurants. Cinque Terre is a few minutes away by train.
we missed the last bus that was at 7:30 by 30 minutes. No schedule was listed anywhere
There is a shuttle and it's only 1.5 euro if you buy tickets at the station but they stop at about 7pm. They are also between an hour and 2 hours apart. 
There are 2 lovely local stores just a 10 minute walk away (worth noting their opening times). It is easy to do the Cinque Terre from the hostel- we managed all 5 towns in a day.
The place is very quiet in May, ideal place to have a rest from big cities. The hostel is small, 8 beds, cooking facilities and Wi-Fi are provided. Everything is clean. There is a big locker for every guest (locks/keys provided) and private key. Francesca is ready to help and give hints you need for your stay. To reach the Hostel you can either take a bus (18-15 or 19-20 in the evening), or go through very nice villages (35 minutes of slow walk up the hill using stairs, you pass through 3 small villages, parts of Framura, they are definitely worth seeing), I preferred this way. The stairs begin on the left of the station (with see behind your back). I went to Cinque Terre on 7-52 train (to Levante if you'd like to buy Cinque Terre card or to Monterosso if you like to take a boat ticket)
It takes about 45min. by foot to the beach, but be careful;the way back up is very exhausting. but it was a pity you cannot find a lot of nice places to eat at.