I would like to get a nice view of the Golden Gate Bridge from Kirby Cove. I am wondering though if there is any sort of parking area near Kirby Cove. I am also wondering if it is jam packed for parking in July.
There's a fairly small amount of parking in two clusters along Conzelman Road near the visa point. From there you can hike down the trail all the way to Kirby Cove (be advised, especially for the way back up, that it's a fairly steep trail).
It may be somewhat rather, but some people only stop to take a few pictures, so if the spaces are full, you could wait a bit and take the space of someone leaving. Failing that, there's a bigger lot just after the underpass and you could walk from there. There is also more parking further down Conzelman Road, such as at the traffic circle or Hawk Hill. Visiting outside of peak visiting periods, especially weekends during the summer, may help avoid crowds and traffic.
Once you're done there, I'd also recommend going a bit further and checking out the lighthouse at lovely Point Bonita. Parking right near the trail to the lighthouse is very limited, but there are other spots in the area.
Disclaimer: I've only done this by bike. I've rented a bike a few times in San Francisco, crossed the bridge and rode up the hill. There are two main parking areas (I believe!) and in the times I've been it would seem likely that you'd be able to park, perhaps if you have to wait a bit for someone to leave after doing a bit of sightseeing. Also, you can park in places on the road up the hill but you might have to walk a bit.
You do get a nice view of the bridge from the top of the hill providing the fog hasn't descended.
Official information including a view you might see:
Some information also available on a tripadvisor thread.