Praia de Centeanes and Praia Grande are both bigger than Carvoeiro beach, Centeanes is closer (about 5 minutes by car from the centre of Carvoeiro) Praia Grande is between Carvoeiro and Ferragudo and about 15 minutes by car, both have parking and snack bars/restaurants but best get there early to make sure you get a parking space.
Ferragudo is nice for a walk round, Silves is lovely, very quaint, ruined castle and cathedral but take comfy shoes, it's all uphill! Caldas de Monchique is nice to get away from the heat and buzz of the coast
There are dolphin watching trips out of portimão and Lagos, water parks at Lagoa and Porches, Zoomarine at Guia, boat trips off the beach that go through the caves - lots to do!
Best ice cream in Carvoeiro, IMHO, is gelados e companhia, with entrances from both the in and out roads
The live music in the square started a week ago, so there's something different every night of the week
The last Sunday in August is the local festival with a procession from the church down through the village, plus there are usually games on the beach during the day
And if anyone's arriving in the next few days, Saturday is Black and White night with lots of different live music and dancing shows throughout the village