Pick one location: Yellowstone/Grand Tetons for example and spend your time there including places along the way. Trying to do too many parks/areas will mean you spend your vacation driving with little time in any one place.
I'm guessing 2-3 days driving from your location to YNP that only leaves you 8-10 days when you get there. Other locations would be Bryce/Zion and possibly North Rim of the Grand Canyon. Yosemite is just too far for that short a vacation. It's my favorite park but it's 4 days from your start. And very hard to get a camping site too---they run a lottery.
BK