I am wondering what it would run(ballpark$$$)for someone with a pilots license to fly me( really me and my wife and some gear) to the closest field to Palo Duro Canyon. How do the rates work for small planes?

You're in sticky legal territory here: it's against FAA regs for a non-commercial pilot to fly someone in the manner you describe.  The FAA considers taking someone where they want to go as flying-for-hire, even if you were to split the cost of the flight instead of paying all of the expenses.  The pilot must be going to that destination themself because of an entirely unrelated matter for it to be legal.

If you could find a pilot who was already going to your destination and was willing to share space in his airplane, expect your half of expenses to run about $1.75/hr. for a 150 mph single-engine, $2.60/hr. for a 200 mph single, and $5.20/hr. for a twin-engine a/c.  (Th9is is calculated using $3.50/gal for av-gas and burn rates of 10, 15, and 30 gallons per hour, respectively).

WOW it seems like everything is illegal these days...
I just thought it would be a neat way to go somewhere instead of the same old way I been doing it.  
You have an idea on rates for a commercial pilot to do the same trip??
Maybe I could find a bored pilot!!!

No idea on what a charter runs, sorry, but I'd suggest you'd do a lot worse than putting that money towards your own Private Pilot Certificate; it's an experience unlike any other!

el roto is correct, it is against the FARs to fly you for profit.  I also work 6 days a week.  If your serious, I can find someone who is a comericial rated pilot.  as far as prices go you'd have to talk with him about it.

i might be wrong, but the_emu i think might have a comercial liscence.  you may want to ask him.  

On the legal side, "A private pilot may share the operating expenses of a flight with his passengers" F.A.R. 61.118(b).
Note that it does not specify how the expenses are to be shared.  The pilot therefore should contribute 5% of the gas and the rental.
The best idea is to charge your passenger for the ride to the airport, the they fly "free", there is no law that says you can't compensat a driver for a lift somewhere.