Can't help with the gym but for riding I would recommend a place called Vale Navio. Its on the road between Vilamoura and Albufeira and is run by a lively lady called Georgie.

The Stables
Vale Navio
Albufeira
Tel: 289 542870

The riding centre in Vilamoura is currently closed for refurbishment and won't be open until next year.

There are several down towards Almancil, look out for proper BHS qualified instructors. I think the closest to Vilamoura is one called Quinta dos Amigos.

http://www.equus-algarve.com/QuintadosAmigos/index.htm

I agree with Manuel Vale Navio riding centre is ok they are BHS qualified, in fact its about 600yards up the road from my house, spent many a happy hour there but am going back a few years, have lost my confidence riding horses now cos getting old and ancient mi bottle has gone. Cheers Jayjan