Park is Nice, Campground is Average
Napa only has a few nearby camping options, so having Skyline is a good thing. The park itself has some great trails, as well as a disc golf course and native plant garden. The campground is pretty much just a grassy field, so nothing too special about it--but if you come with good company and make use of the park you can have a very nice time.
A lot of the available space does not have shade--so consider bringing a shade structure. There are both RV and tent options.
It gets very dry and hot later in the season, so I would also recommend spring camping here. Plus, then you can enjoy the wildflowers on the trails.
The park did burn in the October 2017 wildfires, but volunteers have worked hard to get the trails back in shape and open again. The campground and surrounding area did not burn.