The long, hot summers stretch out into October, so you'll get lots of sun at this time, along with thinner crowds.
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Most of the seasonal hotels remain open until the beginning of November and offer some good rates in October and, with the average temperature reaching the mid-20s, there's still enough sun to be soaking up those rays on the beach during the day – just remember to take a jacket out with you in the evenings!
Andalucia consistently ranks as the hottest place in Spain in October. It's warm enough to rent a villa with private pool and you'll find rates are considerably lower than in summer – just make sure there's a terrace where you can sit outside and barbecue dinner.
HOW LONG TO STAY IN MENORCA. Menorca is quite a big island (about 690sqkm), so I would recommend staying on the island at least for 5 days to a full week if you would like to explore it and visit most of the sights at a relaxed pace. Despite its size, driving around the island is quite easy as it is mainly flat.
It's all possible in Spain. The Costa del Sol and the Cabo de Gata in Andalusia, the Canary Islands, and the Costa Blanca are all destinations where you'll find a climate of eternal springtime practically all year round. You'll find it perfectly possible to take a dip at the beach and then relax in the sun.
I definitely think it will be warm enough for sea swimming. Many of the hotel/apartment pools are heated otherwise they might colder than the sea if not in direct sun. You might be mindful of the strength of the sun in Oct with young children.