Disclaimer: don't try this with a newborn, but once your kids are a bit older (I'm currently running with a 2-year-old), try to go off the road!
I have developed a passion for TRAIL RUNNING and actually managed to win my age group in the EX2 Adventures Backyard Burn 10-mile Trail Running series this spring BUT I still do the large majority of my running with my daughter in a jogger. Much can be accomplished running up and down paved hills, but don't shy away from getting off the paved paths!
What are the benefits of trail running? It gets you away from traffic - both the hazards of motor vehicles and the fumes, it is so much quieter, and there is often more to look at. We pass people walking dogs, we have seen birds, ducks, geese, squirrels, storks, turtles, frogs, snakes, foxes, deer, caterpillars, butterflies, and more. The terrain can also be more exciting for your child. We do up and down and through curvy turns. The occasional bump, bump, bump is fun!
Where to go? There are, of course, a variety of levels. Here in Northern Virginia, there are SO MANY choices. Burke Lake Park, for example, is a partially paved and partially packed dirt, fairly level trail that circumnavigates the lake in a 4.5 mile loop. This is a path oft-traveled by our local See Mommy Run group. The recently renovated Cross County Trail has both paved and unpaved sections as well. Part of that trail also skirts Lake Accotink with the much-enjoyed waterfall! There is also the C&O canal and the WO&D path. Even Wakefield Park in Annandale is passable with a stroller with a little upper-body strength :) If you are feeling really adventurous, you can often follow underneath power lines and telephone lines. I'm told that the telephone lines passing next to our house go all the way to Richmond! I haven't yet brought the stroller to Fountainhead, but I'm game to try.