$1000- you are looking at used for a high quality tandem. Take a look at Craig's List and eBay.
We recently purchased a '94 Trek T50 tandem. All of the first generation Trek Tandems (through early 2000s) had the same frame: Chrome-Moly, made in the USA, and are very stiff, though a bit heavy (~40lbs). They are easy to customize, and have more stoker length than some of the other tandems. The current Trek tandem (IMHO) is not worth it.
We also considered a new Mongoose AL Wanderer (do a search on this forum for more information), but when we added up what we would change, versus the overall cost of the used T50, we went with the T50. I also prefer the Chrome-Moly to Aluminum; but you may be the opposite.
Now is a good time to purchase used, with the economy still down. If you choose to purchase used, leave some of your budget for changes/upgrades.
Critical on a tandem is the rigidity of the connection between the two bottom brackets. Look for a very large oval tube or two large tubes connecting them.