Hi Peter,
It will take you an hour to get there from Cudillero, that's all.
There are plenty of hotels in Cudi but sadly, not many places to park. You will most likely have to park on the sea wall or wharfe. Having said that it's not somewhere that you need to worry too much about your bikes.
My lot stay in
http://www.hotelvalle.org/ this place which is about 5 miles west of Cudillero. The hotel is cosy and they offer indoor parking (not for security, but for weather). The food in the hotel is top notch and offers menu of the day or a la carte. They are very nice too.
If you want to go into Cudillero from there (which I do recommend) then it's either a 5 minute blatt down the A8 or, better, an entertaining 15 minute ride along a nice twisty road, the N632. Be advised, the closer you are to the ramp the higher the price of food and beverages. El Remo is the cider place (next to the old fish market - small white building) and they will even pour it for you. The food is excellent too! Most of the other bars do not serve cider except the ramp ones or the ones more inland.
If you want to leave the bikes in Soto and have a drink, then ask for Oscar, the local cabbie. +34629233665. Tell him he was recommended to you by me. (he knows me as Freddy)
In Soto (where the hotel is) there is a good walk to the nearest beach called San Pedro. There is another very pleasant one to a village called San Cosme where you will, frustatingly, find a bar which will not serve you unless you are a guest in the hotel. As you (seem to) like walking, it's a good way to stretch your legs and both walks are a mere 3-4 miles return.
Another Alternative is this hotel:
http://hotelcabovidio.com/ which is slightly more expensive but the restaurant is one of the best around (but not the cheapest). From here it's about 2-3 miles to the lighthouse my GGF built and you can do the coastal walk long the cliffs. Don't be tempted to go around the LH on the RHS. When I was a stupid kid I rode around it on my bicycle
. In the village you have El Cafe for tapas style (Very, very good), or El Regueirin (not Sundays) which is also excellent. Recommend the Salmon, ham, lettuce and tomato salad.
A few short minutes along the N632 (towards Cudi) underneath a double bridge (the old and the new) is a very sharp left hand corner after a long straight. There (on the left) is a short dirt track that will take you to a car park. If you leave the bikes there and take the wooden walkway it will take you to La Concha de Artedo (beach). There is a bar there on the sea wall.
If you return to Cudi/Soto or, better still, if you go to Luarca, Tapia or anywhere around that area, then take the N634 (La Espina) road. It's a nice road with sweeping open bends.
HTH