1968 Buick Riviera, Should I take it?

You should be all over this car. Not only is it a vastly underrated muscle car, these have become collectible and are worth some money along with being pretty to look at.

I'd change the oil/filter, make sure the belts and tires are in good shape, and give it a 20 mile test hop. If it's ok after 20 miles it should be fine for the trip back.

Back in the 70s I drove a 1960 Chrysler New Yorker from CA to OK and I bought that car for 10 dollars; running good and with a clear title and current tag. It wasn't a problem.