I grew up near there, and I used to hunt a couple of ranches a few miles from the park and bordering the park. I take it you drew in the adult hunt in mid-December. They'll be rutting by then, so that will help. If it doesn't rain soon, there won't be any wheat fields on the neighbors. Just find the does, and the bucks will find you. They get really stupid in the rut.
My son drew the #1 permit for the youth hunt at the end of December, so we'll be hunting there this year too. It's been a long time since I hunted up there, so we're really looking forward to it.
Be prepared for a real hunt in really ROUGH country. If you kill one, you will probably be packing him up and down some rugged and steep canyon country, unless you get lucky enough to kill one on a flat trail close to a road. You could see a big one just about anywhere in the park. I don't think there is a bad area to hunt. A few (very few) spots might be a little easier to hike in and out of. The vast majority of that country is just incredibly rugged.
Take some good optics, get a good vantage point and glass a lot. When you've glassed everything and found nothing, then carefully move to another vantage point. Don't silhouette yourself on the skyline. Stay just below the top of the hill you're on, and stay in front of or behind some brush to break up your outline. Stay in the shade as much as possible. Try to keep the sun at your back if you can. If you spot a shooter, it's best if you have a buddy that can stay put and glass while you drop down for a stalk. Plan your route before you take off. Use hand signals with your buddy to keep up with the deer and his movements.
Don't shoot unless you REALLY want him, because it will turn into work real fast after you pull the trigger.