The Calabasas "Bark Park" is located at 4232 Las Virgenes Road. To get there from the 101, take Las Virgenes Road south just under a mile. The entrance is on the left (east). If you're going fast, it is easy to miss it. It's a nice, local dog park open 5am to 9pm with a plenty of space for the doggies as well as a separate gated kids' play area and plenty of parking.
Bark Park was closed after the Woolsey Fire of November 2018 but is now (as of April 2019) partially reopened.
Trailhead to the Bark Park Trail is on the north side of the park.On the north side of the park is the trailhead to the Bark Park Trail, a 1.2 mile climb that links you up with the New Millenium Loop Trail. Round trip you're talking about a 2 1/2 mile hike.
It is a nicely maintained trail with a steady, uphill climb, which means that the way back is a lot quicker than the way up. I would call it a moderate climb for the most part. A good walk to take the kids on. But it can get a bit hot up here, so bring water and sunscreen on summer days.
As you can see from the sign, there's a lot more exploring you can do on these nicely maintained trails in Calabasas.
A view of the Bark Park from the trail above.More on the Bark Park at www.cityofcalabasas.com/recreation/barkpark.html.