It's worth the money to get a CarFax report. You'll get a service history, list of locations it was registered to, how many owners.
Seeing where it's been is important. My car has been a north east car it's entire life, so the first thing I looked for was rust. I was very lucky.
If you're buying a convertible, check the seam around the rear glass. Make sure it's not re-glued or falling in. Also check the seams on the rear sides for splits.
Test the top operation, make sure it works up and down. Make sure you have both key fobs if possible. Test drive the car with the radio off and listen for any odd noises.