September and October are very good months for cycletours in Spain. Not so hot like July/August but warm enough for using short/short. Or in the period from March to June.
Perhaps take a trip to the Spanish inland. Very little traffic on quite roads. Stop at a vineyard and taste the local wine. Alicante Bike Hire have tested routes from Torrevieja/Alicante area and into the inland. We can arrange everything for you with routes, hotels,bikes and equipment for your luggage. One of our hotels is Casa Boquera in Yecla, a boutique hotel, restaurant and winery. They have 11 luxury rooms with private terraces, and the restaurant is driven by a Michelin chef. We use Cannondale road or hybrid bikes, and the luggage is at the minimum. Distance and heightmeters according to your level. Take contact for more info.