Betsy's suggestion of the Boronda Trail up to Timber Top is a good one, although it's mostly through open grassland so there could be a gazillion foxtails around if that's a concern for you. Also, about halfway up that route you'll reach a place where the road/trail forks under a large live oak in a flat grassy meadow. The spur to the left is the lesser used one and it leads a short ways down to good water in Lafler Canyon, which your dogs might really enjoy if it's a warm day. Going right at the fork takes you up to the ridge, but don't expect any more water unless you go to Cold Spring.
Another great trail would be the Little Sur Trail, which begins about 4 miles in on the Old Coast Road (which leaves Highway 1 directly across from the entrance to Andrew Molera SP). The first few miles are through shady redwood forest with plenty of opportunities for your dogs to access the river if it's a warm day, then it's pretty open and sunny and dry all the way to Pico Blanco Camp where there's plenty of water.
And finally, the Kirk Creek Trail to Vicente Flat would be good, although a bit of a drive from your campsite. But the trail's been worked recently and is in great shape the whole way. There's water about at about the halfway point just past Espinosa Camp, and again when you arrive at Vicente Flat.