You can make several trips to Mexico and have a lot of fun for what you'll spend on a Corvette and insurance. My biggest hurdle, as yours will be, is the time it takes to get to the border. Shizzman makes some good points ( he usually does) about Veracruz. You could cross at either McAllen or Brownsville and ride on down to Tampico and then to Veracruz. On the way back stop in Papantla and see some nice Mayan ruins at El Tajin.
Veracruz has some nice restaurants and a nice square.
I got tired of being here, so now I'm there