Al Dana Club(next to Khalifa stadium) and the sheraton i know for sure have indoor courts if you want to beat the heat and almost all the hotels have regular socials so...yeh :)

As for sports shops Sportmart (opposite the Centre...next ot ramada) is good and also Sun and Sand sport on the 3rd floor of the City Centre(Carrefour side) infact that whole 3rd floor is full of sports shops on both sides :)