Before you pack up the minivan and head out, do a little investigating on the Internet and checkout some of the running venues where you'll be staying. USATF has a great site where you can check out running routes that runners all over the U.S. have mapped out as well as map out your own local routes to leave for others to find. MapMyRun.com is another great site for finding running routes of runners across the country. Athlinks.com is a great site for connecting with other runners. I have used Athlinks to find running groups in the cities I've visited for business trips. Just search members by state. Then you can select various Athlinks members from the city you'll be visiting and email them about the best running routes in their area. You might even want to ask if there are any scheduled group runs in the area in which you can participate while you're in town. Some other great sites to connect with fellow runners include Dailymile.com, running-network.com, and RunnersLounge.com.
Not tech-savvy? Not to worry. May take a little more leg work, but call the hotel or campground where you'll be staying and ask if there are greenways and/or running trails in the area. Or better yet ask them if there are any running clubs in the area that you can contact. You also could contact the Parks and Recreation Departments in the areas you'll be staying to see if they have any info that would be helpful.
Once I was at a conference in San Antonio, TX. My hotel was along the Riverwalk. I had some free time one morning and asked at the front desk if there were any running trails/routes in the area. The nice lady behind the desk said, "Sure!" as she handed me a sheet of paper showing me a running route along the Riverwalk and through a nearby neighborhood. I ran the route and had a great run. The neighborhood was actually an old historic neighborhood with huge old Victorian-style homes. I could have just run on the treadmill in the hotel fitness room, but ended up having a great time running along the river and exploring that neighborhood and it all started by asking a simple question at the front desk.
Something I'd like to try sometime (probably after the kids are grown) is a running vacation. There are actually several services that provide running vacations such as RunningVacation.com, and RunningAway.com. You can also check in with your local travel agency to find out about other running-related trips or tours. Or maybe you want to boost your training and participate in something a little more intense such as a running camp or one of Jeff Galloway retreats.
Inevitably, while running in a new place, you're going to meet new people, fellow runners, and possibly make some lasting friendships. So, hit the trials while on the road!