Heated pools tend to be few and far between on the Costa Brava, as the season is short. However, we use the pool until the end of the month and the sea temperatures are warmer in October than in May, currently 20'C. Air temperatures at the end of the month are in the low 20's, yesterday the high was 26' and low 17'c. Obvs will drop later on.
If you are expecting the same vibe as during the summer, you will be disappointed, as many tourist attractions close. i.e. no sunbed rentals, water sports etc. on the beach or water parks, go karts etc. However, there is still lots to see and do in this beautiful region.
The central Costa Brava is the coast you see on the advertising posters, with turquoise water and cove beaches. If that is what you are looking for, take a look around Begur, Calella de Palafrugell etc.
It will be quiet, but not only is it half-term for UK schools, the French have a two week break for Toussaint, and 1st November is a public holiday for Catalonia, so many Catalans will take a long weekend away. This area has many second-home owners, from the Barcelona region.
I recommend you rent a car, so you can explore and you will find at this time of year, the price for a weeks rental from the airport will likely be cheaper than you pay for a transfer to a resort.
Besalu has already been recommended and Girona is great for a day, especially if you are a Game of Thrones fan. Fans of Dali visit the Theatre Museum in Figueres, his house in Port Lligat near Cadaques and also Gala's house in Pubol.
The region is dotted with medieval towns and villages, the most popular tend to be Pals and Peratallada. My favourite is Sant Marti D'Empuries, a tiny village, just a short walk from the Greco-Roman ruins at Empuries, excavated just behind beautiful bays with nice beaches. Nearby L'Escala has a recently renovated old port area in the old town...Just a few ideas!
Oh, and you can get to Barcelona from Girona, for a day trip by train in 38 minutes on the AVE (like TGV) service...