Fifteen years is a long time, especially if the vehicle is already three years old at the start. As others have said, anything European usually gets expensive well before that point. If you really are going to hold on to a vehicle until it is 18+ years old, it's hard to argue against an Acura/Honda or Lexus/Toyota.
Toyotas might be ruled out by crash test scores--they haven't been doing great on the new small overlap test. This is mostly a concern if you frequently drive on two-lane roads at fairly high speeds.
I really like the new Acura MDX, but it's well over you price limit since it's new. The old one is a little dated, but still might be the closest fit for what you're looking for.
One quasi-SUV that might work for you is the Honda Crosstour, which is essentially a tall Accord hatchback. The 2013 picked up some additional safety features, including forward collision alert, lane departure warning, and a passenger side rearview camera.
You're probably over Hyundais by now. And I'm not sure how well the latest ones will go 15-18 years. (They're certainly better than ten years ago.) But with a Santa Fe you'd at least have 10/100 coverage on the powertrain, and the 2013 is fairly luxurious. But it doesn't have as many safety features as the Crosstour.
Subarus tend to be reliable up to about 100,000 miles. After that point past generations have tended to get a little expensive to keep up. The new ones could be better--no head gasket issues would be a good start--but it's far too soon to say with any certainty.
Otherwise, a Subaru Forester could be a very good fit. Extensive safety features that tested well, even in the small overlap test. The only negatives with it are styling (which some people are okay with) and little sense of luxury.
Same with the 2010-2014 Outback.The 2015 Outback could be much more luxurious, I haven't been inside one yet. A loaded new one could be over your cap.
A few comments on Tom's suggestions:
The large GM crossovers (including the Enclave) have a poor reliability record.
The RDX is a nice vehicle, but doesn't have many electronic safety aids.
The Highlander should also check off most boxes, but didn't do well in the small overlap test mentioned above. To be fair, some of the other vehicles discussed here haven't yet been tested, and could do no better, or even worse. The Kia Sorento, related to the Santa Fe, received a "poor" rating in this particular test.