Historically the site holds a few interesting things, but for the average non-archaeologist type you'll probably most appreciate the graveyard with it's stunning marble headstones. The most famous of all of these headstones is the giant bull. There are two ways to explore the graveyard, you can either see the original marble statues in the museum, or walk through the graveyard and check out some beautiful reproductions in their original settings. I recommend doing both, start with the walk through the graveyard, and cool off in the museum.
Once you've finished off in the museum it's well worth exploring the second part of the Kerameikos site with pathways, part of an ancient wall, and several religious sites. This area may not appeal to you on the artistic side the same way as the graveyard, however the walk is very pleasant and it gives you an idea of the landscape on the outer part of ancient Athens.
If you decide that this is a site you want to check out, you simple have to walk about 15 minutes from Thesio Metro Station and you're there. Also make sure to bring your ticket from your visit to the Acropolis, as your ticket will give you access to Kerameikos as well.
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