If you want guaranteed sunshine in October I’d be avoiding the northern side of the island, it’s getting just into cloudy season for that part of the island. In the south you could look at El Medano, it’s a very chilled out seaside town with great beaches, but can be windy (it’s the main wind surf spot for the island), but definitely worth a look. I’d avoid Costa del Silencio and to some degree Las Galletas, too many problems with low level crime there at the moment. You then get to Golf del Sur which is OK but no great beaches and not much else unless you play golf, plus it’s bang on the landing path for the airport. You’ve got Palmmar, small area of self catering, very quiet with some nice restaurants, but again, not much of a beach. After that you’re into the main over populated areas of Los Cristisnos and Las Americas, the further south you get into Costa Adeje you get the more upmarket (expensive) it becomes, but it’s still very built up, just 5* stuff instead. After that you’re into lesser known resorts of Playa Paraiso and Callao Salvaje, again beach is limited. Playa San Juan and Los Gigantes are the last ones on this side. Still heavily built up, but the clientele tends to be at the older end of the spectrum. San Juan has a decent beach, I’ve not tried Los Gigantes beach but it’s supposed to be ok too.
If you’re after road riding you’ll find some great routes with the monster 50km climb from Cristisnos up to the base of Teide being very popular. Traffic can be heavy near the populated coastal areas but soon thins out.
Hope that helps.