An early 80's is 30 years old now, so all the appliances are nearing the end of their useful life. Not that they can't be repaired, but usually the repair cost/problems are more than new ones. So, at minimum, be sure that they all work when you buy it. Refrigerator on both gas and electric, AC unit, water heater, furnace, water pump. If anything does not work, deduct the cost from what you were willing to pay for the rig. Do some research on costs of appliances.
The axels are about at the end of their useful life also and will need replacement soon, if not right now. New ones come with new brakes and bearings which decreases the cost of those items. If the tires are more than 5 years old, new ones will be needed now or very soon.
Look for any evidence of leaks which produce floor rot, one of the banes of all Airstreams. An ice pick is generally used to check for floor rot, especially in the rear end, and near the door and around the front. Floor rot is not easy, nor inexpensive to repair. Any soft spots are a big red flag.
Smell it. Does it smell moldy and damp? look especially hard at the floor condition and for other leaks.
I am NOT trying to discourage you, but you should be well aware of what can go wrong and how much it may cost to repair/update the unit. You want a good experience, not a nightmare which sours you on RV's or Airstreams. So, do your homework and know what you are getting into.
BTW, almost everyone says that you are better off buying an already repaired/updated unit than a well worn one which you put a lot of money into after the purchase. So, look carefully, ask a lot of questions, don't go into it blind. There are quite a number of used larger Airstreams available, so don't worry about finding another, if one is not what you think it should be.
And we welcome you to the Airstream nuthouse.