I go between Dodge City and Garden City in Kansas. It's private, but lots of farmers in the area are more than welcome to let you kill em.
My cousins used to run a pay-per-gun daily p-dog shoot down in Hollis, but after a few years, the numbers dwindled to far to leave enough fun for the rest of the clan. It seems I remember someone else down there doing the same thing, but I can't think of a name. Several places between Childress, TX and Memphis, TX. And the out of state bare bones hunting license is decent
My folks still live in Childress. We used to have them everywhere down there. My Gpa was a county trapper there for years. Sure is a lot of fun shooting those things!
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West oklahoma and north west texas are great for prairie dogs. I personally have hunted them in Midland and Odessa. A but far but worth it.
Western OK, TX or KS or eastern CO. There are lots of them but no one wants to give their personal spots for fear they will be over run and you will be there shooting with your group next year when I want to go. You can get permission. You just have to go out there and do the leg work. Lots of people will let you hunt for free if you just ask. Heck, often neighbors will hear of you being in the area and come looking for you to shoot their dogs too. Your first trip may be more scouting than shooting but after you go out there a time or two you will be set up for a long time. Just load up your guns and ammo and take your kid with you and go do it. The next time you can take your buddies with the land owner's permission. Take pics and let us know how you do.
imhntn is right, you need to plan a scouting trip first to get spots lined up and plan on grippin & grinnin instead of shooting. When I get to hunt pdogs it's way out in the panhandle, I have family that lives out there and they have friends and neighbors that don't mind us shooting dogs either. Just have to be safe & courteous, always look beyond your target to make sure you aren't shooting things that don't need holes in them.(Cattle, horses, passing vehicles, farm implements, etc.) No one wants the little buggers so as long as you are safe & respectful I can't imagine it'll be too tough to get yourself some spots.
+1 call the chamber of commerce in Amarillo also check follett tx as well as Boise city ok lots of prarie poodles to be shot out that way. As far as gear a shooting mat (or old sleeping bag) shooting bags and a spotting scope are essential. I lay prone on the back of a pickup bed a lot and have also used portable benches with good results. I'd offer to let you tag along but sadly I'm sworn to secrecy as to the locations I go, and have stern warnings that no "guests or tourists" allowed. Google some outfitters in either panhandle and some if not most will offer info on p dog shooting. And a kid would always be welcome on the prarie poodle killing fields IMO. Be prepared for long shots and waiting. Also if you go for a full day or multiple days bring your cleaning stuff also as you will likely (if its a good town) fire lots and lots of rounds.
Anywhere in the Panhandle has lots of prairie dogs. You just have to find the right people that will let you hunt their land. A lot of the landowners won't let people unless they know your family real good. I have no idea who you could contact though. 
A lot of great advice! I appreciate all the help on this. Just trying to get into a sport a little late in life and its proven tough with work, kids, etc. plus, I want my son and daughter to be able to know more about this stuff than I did at that age.
