Last cross country trip was last summer from San Jose to DC via 80.
Gotta have: Wash cloth. You can freshen up at many rest rooms and rest stops with just a wash cloth. The soap from dispensers work in a pinch. When you're on the road for hours and hours each day, a damp wash cloth works wonders (keep it a little soap on it). Even if you're stuck at a place with only a drinking fountain or hand sink... you can still freshen up.
Bring your own soap. For places without soap dispensers, a bar of soap and that wash cloth helps greatly.
Truck stops aren't bad these days, especially the ones with showers. For a few bucks ($4-7) you get a nice shower, includes soap, shampoo and a clean dry towel. Doesn't hurt to call/plan ahead as some places are booked. Some places (e.g. the Ohio turnpike on I-80 IIRC) have "trucker" facilities which include a locking restroom/shower which is kept nice and clean by the gov't and are free. If you're not sure if they have one, ask. Pretty much if it says "truck stop" even if it's a hole in the wall, it may have shower facilities.
Flip flops. I may not think certain truck stops aren't that bad, but a pair of flip flops makes you feel secure.
An ice chest. Many places let you load up on ice and an ice chest will help keep your drinks cool and provide a ready source of water for the aformentioned washcloth.
I didn't bother with a sleeping pad/air mattress. Just a sleeping bag in the back was good enough. When you pull over because you're tired, you'll sleep anywhere. The sun WILL awaken you if you're not used to it and the inside of your 4Runner will warm up so park in the shade even if it's the middle of the night and away from the main portions (e.g. if you stop at a rest stop, park AWAY from the rest rooms). You may find that flipping down the sun visors helps a little.
Didn't need it, but pack pepto and a gun (or two). Arby's always sat easy (non-greasy roast beef sandwiches at $.99 and condiments galore) and pretty much exists everywhere.
Gas is cheapest at the truck stops and the best truck stops are usually at the outskirts of towns. Truck stops do lose power so if you're the unlucky sort, you could be stranded for up to a day while they figure out their genny (saw it happen twice around SLC).
Eastern NV is boring BUT don't speed too much. Lots of NHP (its my current state). Nebraska cops are bored and will issue fix it tickets (e.g. no front license plate).