Obviously, hygiene is the main factor. It can't just look clean.
Things like body fats in the showers, steam rooms etc.
I wouldn't get involved in cleaning anything 'poolside' as it's a specialist job and it could become quite expensive if they had to drain the pool!
In the fitness rooms, gym equipment should be washed because although they will 'look' clean the equipment will be covered in sweat.
Access could be a problem as hotel leisure centres tend to open 7 am to 10 pm.
personally, I would try and persuade them to have a cleaner attend for a full day shift rather than a couple of part time shifts. It would be far easier to recruit.
The main thing is to get a 'specification' off the Client and I'd be glad to have a look at it if it's faxable.