Hi Kenneth. I applaud your road trip ambitions, but just want to point out it will take you three days (driving over 10 hours each day) just to get to Yellowstone NP from New York – and of course, 3 days back. So even though 15 days sounds like a long time, your time to enjoy the park will be limited to 9 days or less. Now that should be plenty of time, to see and do most things you'll want to, plus the Grand Tetons and Jackson, Wyoming (which, if you're driving all that way, you'll also want to do). I would highly suggest at least 2 or 3 days for Badlands NP and the Black Hills in South Dakota, and Devil's Tower in eastern Wyoming since they are on the way. Do your homework ahead of time and learn about the park at nps.gov, and also search for info here, lots of people have already written about Yellowstone including me! Be aware that travelling with your dog will limit where you can go inside Yellowstone (and probably other parks as well).