Have a 99 z24 Cavalier, 2.4L, automatic.
Currently have 16 inch wheels with P20555R16 tires, rides like a tank.
Tires due for replacement.and
considering going to 15 inch wheels with narrower tires to improve
ride characteristics, not sure what problems I may encounter.
Any suggestions
Thanks

These cars (not the Z/24, though) also came from the factory with 14" and 15" wheels. The 15's were 15x6, I believe, and came with P195/65R-15 tires, which would be very close to the same diameter as what you have with the 16's, so that the speedometer would remain pretty much accurate. There should be no problems with fitment on them. The problem is, the factory 15" alloys may be hard to find, most of them were steelies with wheel covers, so if you don't mind that, there should be tons of them in boneyards.

check ebay they are a dime a dozen