Anywhere you can recomend in or around Luchon and in Sierra Nevada also hotelwise
Luchon has quite a few nice hotels in town, its a spa town so quite a popular tourist resort. We usually stay in the arome vanille campsite which has cabins available. They’re pretty basic more like a large caravan without wheels but more space than a hotel room and fairly cheap. Its easy to DIY a trip as there are lots of well marked routes and good maps and a 1200m bubble lift. A week or so would be enough even you mix it up a bit and do some walking and rafting so you might need a second venue, maybe Andorra or one of the other ski resorts.
For Sierra Nevada you probably need to go with a tour company. I’ve not been out there for a few years so better advice above.