In your case, the longer you stay off of it, the better. I would say at least 5 days. If you stretch it to a week, that's even better.
Currently, in my area, the water folks have enacted a voluntary water-saving program. We're asked not to water our lawns (which I don't do anyway) and we're asked not to wash our cars (which, sadly, I don't do either). My point is, if you're in a drought situation, DON'T do what I'm about to suggest.
You can help the curing process by wetting the blacktop a bit. When it's very hot outside, it will repeatedly 'move' and settle over a number of days. By wetting it, you 'solidify' it in place. You don't have to wet it to the point where the driveway is submerged. Just wet it enough so that the water isn't evaporating off of it too quickly. If 10 minutes goes by and it's still wet, you've soaked it enough. Do this at dusk; not in the morning.
If you had your driveway layed in the fall, the cooler it is outside, the better. Hot asphalt will 'solidify' quicker in cooler weather. Usually, at this time of year, you can park on it after 2 or 3 days. Hence, for future reference, settling time can vary. Also, for future reference, ask your contractor this question. In fact, you should be able to call him now. Over time, the weight of your cars (and such) will depress the driveway a bit for obvious reasons no matter how long you wait. Unless you can apply equal pressure all over your driveway, you will see a difference where the tires have been driven. As long as there isn't any very noticable difference, don't worry 'bout it. Hopefully, your new driveway slopes AWAY from your house/garage.
And lastly, my unsolicited $.02 says that this time next year, you ought to seal it. After the driveway has gone through 4 seasons, you should seal it up. Pick a hot day and start before sunrise. I suggest the pre-packaged, 'gritty' sealer (sand-sealer). It's hard to mix so get yourself a few mixing sticks. (You may break one or 2.) This stuff will fill small depressions and cracks while leaving a slightly 'gritty' surface to help with traction in rain or snow. Once you're sealed it, ONLY seal it when you start to see the 'white' of the stone. If you do it too often, you'll end up with a driveway of gooh!!! It will be in the house on the floors and in your cars. One of my neighbors had to have his driveway re-done because he use to seal it every 2 years whether it needed it or not. Sure, it looked nice but it was counter-productive. Again, you can ask your contractor about care instructions too.