> we suspect that many people who have access to private jets will immediately take to the skies and escape city centers.

I would bet on the exact opposite. Unless you're within a few hundred meters of ground zero you're better off seeking shelter than trying to run, and if you are running you only want to go those few hundred meters and then take shelter. The local airport where your plane presumably is would be far more likely to be targeted than your current location. Traveling to the airport, especially in the chaos of people scrambling for shelter, is probably going to take much longer than you have time for and you are much more exposed than if you went into a basement/subway/concrete stairwell. Even if you could physically get to the airport in time, that doesn't do you much good if the plane isn't ready to go. If the plane is on hot-standby you might be able to take off within 10 minutes of getting to the airport, but if we're assuming this is a sudden development you gotta get the crew to the plane, you need to fuel the plane, etc; you're not getting off the ground in less than half an hour. If by some miracle you could get up in the air before the nuke hit, the air is the worst possible place to be. There is nothing between your plane and the pressure wave of the nuke. Your plane's electronics are going to get fried by EMPs. There's a decent chance your pilot will go blind depending on where the nuke actually hits. Even if you manage to stay in the air - now what? You need to land eventually. Most airports have been destroyed, and air traffic control is probably down or at best too busy to deal with you so you don't know if you're actually going to be able to land at any particular destination. Absolute best case scenario you land in a random location where everyone of the ground is several hours ahead of you into a SHTF situation.

I'm not saying nobody will try it, but I would think most people with access to private jets probably have access to or could acquire access to basements in well built buildings that are a decent bit away from likely targets of nuclear strikes.