Everyone has their favorites; I love lots of the more exciting rides, but will talk about what I consider a few "musts but off the beaten tracks" for me.
I love Turtle Talk with Crush at Epcot, because of the way that there is realistic interaction with the audience. You can search YouTube to get an idea. It is a great way to cool off, funny, not a big line, and a great way to get a little "rest." The interaction is really funny.
I also enjoy Monster's Inc Laugh Floor, for the same reasons, but it is not everyone's cup of tea.
I always make sure to ride the Tomorrowland Transit Authority People Mover at night, because of how lovely the views are of the park at night - a quiet way to have a pleasant ride and cool off a little (you go inside some of the buildings, can see the Buzz Lightyear ride, etc.). It is very retro. I also HIGHLY recommend riding the rides during the parades, as the waits are much shorter - I've run down the ramp/walked right onto Pirates, as well as onto Splash Mountain. I strongly believe that Splash Mountain should be done after dark, as just as you hit the crest of the drop, you get a quick view of the Castle all lit up, then you drop. It is a moment of beauty.
Food can be expensive there. Since it is a first visit, keep your eye open for possible "Free Dining" - If it is offered, I would consider upgrading for $20 a day for the Regular Dining Plan, if you want to try some of their sit down restaurants/character meals. You could then do a character dining or two, eat at a few signature restaurants (you would use two table credits for a signature restaurant).
Have you considered a split-stay? The resorts are part of the experience. Trying two different resorts is very doable in your amount of time there. If you don't have a car, Bell Services will transfer your luggage. You could try out a couple of different value resorts, or even part of your time at a value resort, and see if there are any "value" rooms available at Animal Kingdom Lodge/Jambo House in a villa (rent points through a broker, like David's DVC.) While it is $150 a night, it includes tax. Tax for The Movies resort is 13.5%. $7 more a night to stay at the Lodge (for less than $100 you could stay there for your entire trip). A villa studio would include a microwave and a mini fridge, coffee maker, other small amenities. This would not include free dining, but if you split your stay, you could do free dining (if offered) at the value, then switch over to AKL, renting points for a few nights. The pool at Kidani (next to Jambo House, but the value rooms are in Jambo) has a great slide, and you would be able to use it. There is so much to see at Jambo as well, for during your "down time."
Absolutely try and visit some of the Deluxe resorts, just for the experience. The theming of some of them is amazing. You could do a Monorail dinner, having an appetizer at the Contemporary, entree at the Polynesian, dessert over at the Grand Floridian, then over to MK for Extended Hours. If you are of drinking age, I'd recommend Trader Sam's Grog Grotto at the Poly, if not, then try a Dole Whip. Or even a quick breakfast at the Polynesian Captain Cook's and try the Tonga Toast, then take a little boat over to the MK. We really enjoyed dinner over at Wilderness Lodge, then taking a boat, and were treated to the Electrical Water Pageant on our way to MK.
