there are a couple of 'pure' gyms i know of SAS Gym and Gold's Gym (this one you may not know of it unless you are American) which cater for the gym freaks ... the latter gym i believe is spoofed in Dodgeball (w/ Ben Stiller and Will Farrell)

However, there are a few that are health clubs which is what you are after in your description they are:-

Al Dana Club
Diplomatic Club
Doha Club (but closing soon)
and clubs in major hotels
Intercon
Ramada
Ritz
Sheraton etc
plus Al Sharq Ritz Carlton opening soon and some other hotels

I think most are pretty full. Prices for singles range from 3000qr to 8000qr per year appr.

Do not know of any with climbing walls.

Can I ask do the numerous stadiums have gyms that can be used. Also, somewhere like Aspire, can you use any of the facilities there?

PLus, many housing compunds have all these facilities ... the quality depends on the compund offcourse, some are real nice such as Mirage, Al Fardan, Beverly Hills, Tbah etc some not so.