Air Bnb is a good place to start, October is still considered high season so try to book as soon as possible.
Alternatively, here are a few hotel recommendations. I have listed quite a few as many of these hotels only have a few rooms.
Hotel
Sicilia Hotel Spa Giarre Catania
444 Via Callipoli Giarre, Sicilia 95014, Italy +39 095 779 2552
Hotel
Kepos Etna Relais
118 Via Leonardo Da Vinci Santa Venerina, Sicilia 95010, Italy +39 347 838 7715
Hotel
Monaci delle Terre Nere
Via Monaci Zafferana Etnea, Sicilia 95019, Italy +39 095 708 3638
Hotel
Hotel Caesar Palace
130 Via Consolare Valeria Chianchitta-pallio, Sicilia 98035, Italy +39 0942 5590
Hotel
Agriturismo il melograno
Hotel
Agriturismo San Leonardello
165 Via Madonna della Libertà Carruba-San Leonardello, Sicilia 95010, Italy 095 964020
Hotel
Palazzo Rosso
11 SP173 Sicilia 95018, Italy 347 554 8759
Hotel
Torre Archirafi
Torre Archirafi, Sicilia 95018, Italy
Hotel
Atlantis Palace Hotel
257 Via Spiaggia Sicilia 95016, Italy 095 782 8947
Hotel
B&B Alhambra
34 Via Luigi Orlando Giarre, Sicilia 95014, Italy 095 932404
Hotel
Oasis Park Hotel
189 Via Spiaggia Mascali, Sicilia 95016, Italy 095 778 4672