I reside here in Pinellas County, and I can confirm that Clearwater Beach traffic in July will be very heavy. Plan on at least 2 1/2 hours each way (if you are lucky) for driving. You will hit bottle necks in Tampa, as well as in Clearwater on the way out to Clearwater Beach.
Having experienced the beaches here, as well as Cocoa Beach, I would recommend Cocoa Beach mainly because you will be staying in Orlando. You will spend less than 1 hour in the car each way, and the beach is just as good as any we have here on the gulf coast. If you want to parasail or rent a jet ski, those are also available at Cocoa Beach.