On the Spanish side of the Pyrenees, Hotel Les Brases in Sort is a good base. Bike friendly, secure lock-up for bikes. Food in the hotel is OK and some nice restaurants in the town
Great loop north via C13 over Col de Bonaigua to Viellha then south to La Pobla de Segur via N230 and N260 then north again back to Sort - about 120 miles.
I've stayed there too - great hotel as you say. Brilliant breakfast with fried eggs straight from the pan!