Caps run in the neighborhood of $125 and up for a good quality stainless one. Cost of labor to install can be as little as $150 to several hundred dollars. What determines this and the cost of the cap is the size of the flue pipe, the height of the chimney and the pitch of the roof if they need to access the chimney from that way.
If your speaking of a fireplace cap with remote damper, the prices can start at $200 for a good cap plus a few hundred dollars for the install. But again, pitch, height all plays a factor in the cost.
What is the reason for the new chimney cap being installed? Old one fall off, or just want to keep the water out?
over 30 years old and leaking into the fireplace, very rusted
By bet is that you have some smoke spillage in front of the fireplace also?
If the fireplace was designed properly, water should really never see the fireplace area at all, unless extreme downpour. But a properly sized cap on top with good quality remote damper would be best.
I suppose it depends on where you live, mine cost $175 but I didn't have to get on the roof so it was worth every cent to me.