1st thing - buy a parking pass NEXT to the great lawn - it used to be the Orange pass, I think they changed the color. Buy your parking pass NOW don't wait....unless you're going to Uber to the game.
2nd - Arrive 3 hours before the game (be AT the stadium) to tailgate...so account for drive time. Even if you don't have food, others will share with you...it's a community. Just say you flew into town for the game and ask 'Hi, we flew in for the game - do you guys have any extra?' The answer will always be 'Yes and where you from" I'd just advise to bring a small throw away cooler with a few of the drinks of your choice. Again, trust me SHOW up 3 hours before - you'll get a great amount of time hanging out and then leave to the game 30 min before it starts to get through security and the ticket lines....allowing you time to go to the restroom and/or get food before the game starts....put a timer on so you leave 30 min before.
I always advise new people to go in 40-50 min early to walk around the stadium and see it from the different areas. If you follow the 3 hours before and the 30 min before walk in you'll be in great shape.
I NEVER understand the people whom show up and just go into the game. The tailgating is often better than the game experience....especially with the great weather you'll have.
Reminder if you have a girl with you NO PURSES ARE ALLOWED. Tell her to leave her purse at home and just take the bare necessities. Again, you will NOT get in if she has a purse.....no matter how much she argues.
Restaurants: Use Yelp - ALWAYS use Yelp the app and you'll find great food....just walking into random places is the dumbest thing you can do....in Phx or any town. Yelp is always the way to go to find great restaurants.
Activities - there's the main stage on the great lawn with music - I'd bring a football to throw around. It's more of a community hang out than it is 'activities' per say. There are tailgates that have games...they'll always let you play if you ask.