I need to know of some good cheap dependable automobiles for a road trip.?

I plan on starting in Cleveland Ohio. Then traveling to Portland Oregon. From there I plan on traveling to San Fransisco Californina. I would continue my travles to Houston Texas than to New Orleans Louisianna. I hope to stop at Mammoth Caves on my way back to Ohio. Is there any automobile out there for less than $10,000 that can do all this driving? My parents say no but I say yes. I was thinking about buying a Mitsubishi Eclipse or a 3000GT or some other sporty two door automobile.