Julison, according to the Airstream weight chart, your '69 Caravel weighs 2880 lbs with a 360 lb tongue weight. That puts it well out of the range of towing it with your Hyundai.
I have towed a '61 Bambi with a '98 Astro. As long as you have good, solid sidewall tires on the Astro, and you use a weight distributing/sway control hitch you'll be amazed at how well an Astro will tow. As a matter of fact, it's almost an ideal tow vehicle IMHO for anything under 3500 lbs dry. It's max tow rating in the AWD version, as I recall, is about 4800 lbs. I wouldn't suggest the 2 WD version as they are really squirelly in reduced traction situations. The AWD version however is like a mule. They're quite remarkable, and the 4.3l V6 is a tried and true workhorse. I only traded my Astro off when I bought my Y2K Excursion, and even now three years later, I still wonder if it was the right thing to do!
AIR 2053 Current: 2006 Born Free 32 RQ Kodiak Chassis, & 1995 Coachmen B-van
Former Airstreams: 1953 Flying Cloud, 1957 Overlander, 1961 Bambi, 1970 Safari Special, 1978 Argosy Minuet, 1985 325 Moho, 1994 Limited 34' Two-door, 1994 B190 "B-Van"