Best Places to Swim in Cairo

I have no idea about prices. I only know places.

In Maadi, you have The Maadi Degla Club.
JW Marriot Hotel, you can go for day use or pay a monthly or yearly subscription.
Gizera Sporting Club in Zamalek.
All the BIG Hotels offer day use and memberships.

The Sofitel in Maadi offers a decent price for swimming in their pool. The Wadi Digla club requires membership, and for non-Egyptians, the price is quite high! There's also the Mohamed Ali Club, you can get memberships or you can enter for one day.

You can swim at the Conrad Hotel and at the Marriott in Zamalek.  You can join or you can pay for day use.  These two are quite pricey but if you use them regularly then its worth it.  The J.W Marriott Mirage City has an indoor and outdoor pool which you can use as part of the "Gym" package and they are heated when the weather turns cooler.

try Arabella Country Club, you can have also the daily use.  It's perfect if you are looking for a quiet place. 
the price is 100 le adult/daily use swimming pool.

When it comes about swimming pools, I think the first thing you have to look for a safety one, that could keep you in healthy conditions!
In this sense you have to have your private pool or better cut a little from your time and enjoy benefits of the seas around!