Looking to climb!

I am taking a trip across southern Utah, hitting some National parks and would love to get some climbing in. I will be in the Moab area from 6/3-6/8 then moving over to the Bryce Canyon and Zion from 6/9-6/12. My schedule is pretty open. To be completely honest, I do not have much experience climbing outdoors but I would love to learn if anyone is willing. I am comfortable climbing up to 5.9s and some 5.10.