The best place to run, functionally speaking, is right in my backyard -- River Road Park in Bedminster, NJ. It's a park that is adjacent to miles upon miles of rolling dirt roads through rural (and affluent) NJ, and has tons of options for runs of all types. Realistically I don't really need anything else other than a few other parks in my area.
Starting off in the park, you run a little bit down the road, and you start to hit the dirt roads. I believe they're still dirt because of all of the horse farms in the area, and I would also guess because the old money locals don't want too many people driving through, which is a plus for runners. The area is beautiful, there is a river to your left and beautiful houses to your right, running right through horse pastures. There's also this nature walk area next to the park that is like a grass XC course, which is great for adding on a mile or two to your run.
Your options start a bit down the dirt road, you can either turn onto Larger Cross Road, cross Lamington Road, and run through there, doing what I've known as "The Lollipop" (on Strava it looks like a lollipop) which is a 10-mile round-trip loop of rolling hills and at least one big climb, depending on how you do it. You can also do a larger 13-14 mile loop if you run towards Pottersville road, make a right, and reconnect with the dirt roads again for more rolling hills. The views on this loop are absolutely incredible, so if you're in shape I highly recommend this one.
If you choose to not make the turn onto Larger Cross, you can run straight down River Road and towards Trump National Golf Course, where a public dirt road runs right through. First you have to get up a massive climb of about 300m to get there, then you descend into the course. Again, you make the right turn onto the main road and re-connect with the dirt roads a little bit down the way -- I believe that loop is 17 miles. On certain days, especially in the winter or on a day when you know not many people are going to be at the course, you can dip into the trespassing zone and run the "Trump Trails," which are miles upon miles of unused horse trails that run behind the course. These range from dirt, to mulch, to grass, to gravel -- very cool. Have only done it once, but it's worth it.
There are a bunch of other spinoff roads that are dirt, but usually end up not looping back or ending in asphalt. Worth exploring, with that caveat.
Here are four of the established loops
River Road 10 miler:
http://www.gmap-pedometer.com/?r=7429562
River Road 13.5 miler:
http://www.gmap-pedometer.com/?r=7429563
River Road Trump 13.9 miler:
http://www.gmap-pedometer.com/?r=7429567
River Road Trump 17 miler:
http://www.gmap-pedometer.com/?r=7429566