hi,
There is a Crossfit gym which does training sessions comprising strength, agility and stamina - not speed per se. Crossfit was developed initilally to train firefighters and forces personnel as it's an 'all round' fitness rather than a focus on one specific sport. The website is
www.crossfitbasel.ch, they all speak English and training is done both in German and English. You train in groups, not independently and it's in Dreispitz. It might be more of what you're looking for rather than a conventional gym, though not focused on running training. Men and women there, all ages, mixed abilities, welcoming environment...