A new Nimitz-class carrier's top speed is 30 knots, but if it were fitted with jets instead of propellers, how much faster would it go?

Not necessarily faster. As has been pointed out already, every hull has a "hull speed" beyond which the drag increases vastly, It is possible to go faster than they hull speed, but effectively you push a wall of water in front of you.

Even if the hull speed is not exceeded, speed is a matter of converting energy into thrust. And a water propeller is actually better than an air propeller (which is what high-bypass jets amount to) at doing that, because the water is thicker. The only time a pure jet has an advantage is when the speed of the craft is approaching the speed of sound, when propellers stop working because the air will no longer flow back into the space they have pushed out from before the propeller comes round again.

To make the carrier go faster, you would need a hull shape designed to go faster, and more raw power. I see no reason why you could not fit bigger nuclear piles and more propellors if you wanted to, but it would be expensive.

Actually the Nimitz-class ships can go much faster than 30 kts, but that's all the Navy will admit to. Like Alec said, a ships speed capability is more a funtion of hull design. +2

This depends more on the capabilities of the jet drive itself than of the engine. Trust me, the POWER is there, but using it is the tricky part.

I can barely imagine a jet drive big enough for the job, or the flow rates involved, or the sheer damage a jet drive that big could do shooting thousands of gallons per second at ridiculous speeds....

How many jet engines? It would take a good number of the largest to even make it go as fast. It would be quite the technological challenge to mount enough of them while maintaining full usability of the deck, not to mention the turbulence created by such thrust for landing aircraft.

Every ship hull has a maximum speed through the water. A seven knot hull will not do more than that speed, even if it driven by a thousand horsepower.

Jets!! Sounds like horse shit to me.