I think an easy fairly flat hike near WW is the "east table mountain" road (that is what the Forest Service called it, I think the locals call it something else). It is halfway up the road to the Table Mountain Campground. There is a big switchback and a pull off where their is a large white pipe (8" well casing pipe) gate. It heads off east back towards WW. The gate is not closed in the summer but is gated in the winter. I hiked it with my dogs a couple of times. It really isn't a "trail" but a lot of folks hike or ride their bikes on it.
This is a great suggestion, if you are looking for something fairly level and shady. I've always called it "McLellan Flat Road". Don't know the official name. It's a road, not a trail, and it's nice because the miles are painted on the pavement, in 1/2 mile increments, I believe. The road is 3 miles to the top, where there is some equipment (JPL I think). The first 2 miles are fairly level, and the last mile steepens. Since the miles are marked, you can turn around at any point and know how far you've gone. Used to be buggy in the summer, but this year has been so dry that the bugs aren't bad at all. Lots of folks walk their dogs on that road.
Yes, you do need an adventure pass to park at McLellan Flat. You can get them at Jensen's and the Mini-Mart, and at Big Pines Ranger Station if it's open. I just get an annual pass and keep it in my glove box, since I'm up there a lot.