Something you may want to consider is to plan your trip for the 10 days, then leave a day or two early. First you have a real long haul, and should something go wrong you will still be good, all it takes is the car to have something or a lost credit card, also on this kind of trip have some emergency cash on you. Just trust me on this. And, if you arrive early you can relax for a day before you hit the town. Or be able to stop at something along the way and not be so worried about staying on a schedule. Just a little built in leasure time. You never know what you will come across on the road, and want to check out.
Since you live in the Seattle area you can go to my favorite luggage maker, Tom Bihn, that I am always talking about, and get something to make the trip easier and more fun.
For or a trip like this, take enough clothes for the entire trip so you are covered, and you don't have to do a wash, then on the day you fly back put your clothes in a box and Fed-Ex them home. This way you have what you need. There is nothing worse than having to do laundry on the road, and at 10 days you will be pretty well packed.
Since the the airlines charge for luggage anyway, I now ship my suitcase to the hotel and back home, and eliminate the airlines from all but my carry on, and it is a great way to travel. Just make sure you can trust the hotel. However, in your case, you are driving the first segment of the trip, and would be shipping outbound to home so you are good. Just don't use the overnight service.
Travel can can be fun, and how you make it a fun, no problem trip is all in the planning. It really is all in the planning. The better you plan, the more enjoyable your trip will be.
Now, GPS...cool, until all of the things that can fail...fail. Go to Wal-Mart and get an atlas, and to AAA so you can have a NYC map. Study them before you depart. You can still use the GPS but, it is nice to have an idea where you are both on the road and in the city. Even the Maps on computers are just not the same as a real map.
Manhattan is easy to get around the streets run east and west while the avenues go north and south. The outer boroughs, I am not very familiar with. However they are great places, too.
I have traveled my entire life, the last almost 40 years on business, which has taken me around the world many times, all on someone else's expense accounts. Which has been wonderful. Plus, I was able to take my wife and daughter around the world.
Hopefully, something here will assist you. There are some other professional travelers here on the forum, I'm sure they will have some good ideas for you.
One more bit of advice, for anyone young is travel now, don't wait until you are older. I'm glad I had the opportunity growing up to have a family that travelled quite a bit, and that I have always been my own boss. Just travel while you are young. It gives you a lifetime of memories, and it is so educational, you learn so much as a traveler. I gained more knowledge traveling than anything I ever did in college.
I know people who are in their 50's just starting to go places, and the world is becoming a much more dangerous place, so see it now, who knows what the future has in store.
That's all for now,
RL