Arizona is a good place to hunt coyotes and bobcats. Lots of public land and lots of predators. From what my friends have told me, Nevada is good also, but the Las Vegas area wouldn't be a good choice.
Here in Western South Dakota is the premier place to shoot prairie dogs. But guide services are expensive and public areas are extremely over-shot. You can get info on praire dog areas from the South Dakota Game and Fish site. Area guides charge $175 a day with a 2 guy, three day minimum. A PD shooting day is 4 hours, with additional time being charged extra. Room and board is also extra. Your other alternative is to hit the small town diners early in the morning and talk to the locals. You can possibly find a town you could shoot for free. As far as coyotes, they are everywhere, hardly anyone hunts them anymore. Good Luck!
unicle buck, crapshoot told you right about the Los Vegas area. Most of Nevada has been shot up in recent years from the air and from the ground. But you may still find a few critters lurking around if you know where to look. The Humboldt river dranage east of Winnemucca can get you a few coyotes so can the Midas area, lots of ground squirrels and badgers in the area too. What use to be a hot spot is north of Winnemucca the Orovada and Denio areas. Maybe you can get Q to tell you where he gets all his coyotes in Nebraska from lol. Uncle buck, I'd say go to Nevada, it's wide open and you'll all have a ball. I believe it to be the last of the wild wild west and buddy it is when you see all that land to hunt on. Small western towns like Austin, Lida, Jiggs, Manhatten and a ton more. It's like steping back more then a 100 years, good luck.