The Eleusis map shows that the site is just 22km (14 miles) west of Athens, so if you have a car it's not difficult to get to. Organised tours are hard to find, and I found the easiest way was by bus public transport. It's best to check on the bus timetable when you're in Athens, because they can easily change. Take the A16 or B16 From Plateia Eleftherias, just north of Monastiraki. They should go every 20 minutes or so. If the traffic isn't too bad you should get there in under 40 minutes.
A taxi is also a possibility, but would be quite expensive.
The site was originally linked to Athens by the 'Sacred Way', but don't try and walk this today. The historian Michael Woods once did a TV program showing where the route lies, and although interesting to watch, I'd rather he did it than me. Too many busy roads involved!
The site is not in a particularly attractive area, as today it finds itself in the middle of an industrial zone. It's actually in the middle of the modern suburb of Elefsina, hemmed in by factories and oil refineries. There aren't any beaches, nice shady avenues, or even tavernas nearby, so don't plan on spending any time outside the site. In face, if you're going to places such as Corinth or Mycenae, you can visit the site on the way because it's just off the old main road between Athens and Corinth.
Map of the area
This map shows you where the site is in relation to Athens (just hover your mouse over the red markers). You can use the controls on the left to zoom in and out of the map, and you can move the map around by holding down your mouse button and moving the mouse around. The "Satellite" view isn't especially interesting as the resolution for the area isn't as detailed as that for Athens itself, although you can make out the Telesterion, the Propylaia and the Museum.