I used to be a member of Modern Club...I think its one of the biggest IF not the biggest in karachi, it has 6 courts + wall practice court + squash court..Location is the intersection of Shahra-e-Faisal and Tipu Sultan Road, as soon as u turn onto Tipu Sultan Road from Shahra-e-Faisal, take the 1st left (right after Habitt) and the club entrance will be on the right...
As far as CHEAP is concerned, it USED to be cheap when I joined it some 10 years ago, one time joining fee of rs 6000 and montly 350 for tennis only ( extra for squash and gym ) I can imagine it would cost a LOT more now