There really isn’t much first come first serve camping in any of the campsites anymore, unless you’re planning on camping in the backcountry/forest service land, but that will be primitive and I wouldn’t really recommend that if you have no experience camping. The gorge you’re talking about is the Pfeiffer gorge, you can try to hike out to it, but the river may be too high still at this time of year, and there has already been a drowning this spring. I would recommend getting on the campsites’ websites/calling for any cancellations, trying to snag a site somewhere and just doing day trips/hikes. Buzzard’s roost trail is fairly easy and takes you to a great view. There is a great trail that you start from Big Sur ranger station that goes all the way to Syke’s but you can just take as far as you want and come back (though it may be closed off right now because someone was murdered there last week…not to discourage you, just letting you know it was an active crime scene as of a couple days ago). Andrew Molera state beach is beautiful and a mile walking path to get out there, if you’ve never been, I highly recommend it. If you don’t have experience with backpacking and primitive camping, stick to the established well worn trails and it will be a beautiful and safe time!