This information is probably out of date but Heinrich Harrer who was the first person to climb the North Face of the Eiger had this same problem whilst living in Tibet. He said that the hot springs were excellent treatment. In Germany, France and other countries Europe etc this is still a 3 week treatment paid for by the health service. By a Jacuzzi/hottub. When they were invented they surely weren't devised just for porn
Potes is your best bet as it is closest to Santander. You could also go to Cangas de Onis the other side of the park which is quite close to Llanes, has the roman bridge and is close to the Lagos de Covadonga which is also worth a visit. Arenas de Cabrales as Cathy says is fine but a little smaller, and maybe a bit too remote for Two teenage girls.
Jim, Don't take the snowshoes as they may not be needed depending on the routes you decide to take. Estaing is small and in the summer most of the shops have packed away the winter gear. But you should be able to hire snowshoes in Argeles as there are a few outdoor shops.
Terry, You're looking at around 10 days going at normal GR10 pace, but as I said that could all change, it's just that there is a huge amount of snow this year and depending on your confidence and experience you could be OK without winter equipment. You don't have to decide yet as a lot can happen in three months.
As Ed says there is loads of info on this forum on kit etc. I used to live in Cauterets and now live in Hendaye (starting a new job in 2 weeks). Usually in June you could expect to find snow on the cols at 2000m. However, this year unless something drastic happens, if starting in June you may need to consider some form of winter equipment (unless starting at the end of the month). There has been an incredible amount of snow this winter. It is normal to have snow at this time of year but earlier on in the season there was so much there will be a lot left around June which could be quite dangerous. If your dates are not fixed I would put of the start date as late as possible, unless you want to caarry snowshoes etc.
I spoke to friends in Cauterets a couple of days ago and there is still 5 metres and more of snow at 2000m which will take a lot of melting. It isn't that cold at the moment but it is still snowing at about 1200m