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IMO the Goodyears are as good as it gets for dry conditions. Having said that, I just swapped them out for a set of Toyo Proxes T1-S (although I'm hanging on to the "old" tires for autocrossing) There are several good options out there but discussions over on the wheels& tires section convinced me the Toyos were the way to go for a good performance tire in wet and dry conditions. Less than 100 miles on them but they handle well (not quite as good as the F1s), they're relatively quiet and they look great on the car.
Give Michelin a try or Yoko AVS Sports. Not sure about what tire fitment there are for the Z06 aside from GY F1 SC. Still too new for the aftermarket manufacturers (and limited numbers too).
BridgeStone Protenza's 03 are a great tire. Kumo's are cheap but life is limited, and no 18's. Spend a lot of money and get a set of BFG kd's they were like iron and take a lot of abuse. Great street tire.