Olympia, Nemea, Delphi and Isthmia made up the Panhellenic cycle of games. While Olympia has a decent museum, the site is less spectacular. It's also the furthest away from the others. I suggest you visit Delphi first--mostly because it's the best site, then Isthmia and Nemea can be done on the same day. Eating beside the Corinth canal is recommended. Go to the bridge over the canal at Isthmia and either look for a restaurant on the far side, or go to the left of the bridge and sit at the seafood restaurant with a terrace right next to the canal.
The athletically inclined will definitely want to take the hike up to Delphi's Stadium. It's one of the most complete examples you'll see (and the site of Delphi is a must-see in any case). Perched on the Delphi's highest point, the stadium could accommodate 7000 spectators. The remains of a Roman triumphal arch are found on one end. You can see the stone cut starting blocks on both ends. Look closely at the walls, there is ancient graffiti there, including a wine prohibition. The stadium is 187 meters long; the track 178 meters.
The Museum at Delphi is open daily 7:30 to 19:00.
The site of Isthmia is an interesting, off-the-beaten-path destination. I worked the summer here, helping restore the Roman baths nearby. From the site you can walk to the Corinth Canal, to a point where there's an amazing bridge over the canal that goes underwater when a large boat passes (and for a real thrill, wait for a huge cruise ship to come through with just a few feet separating it from the wall you're standing on). There are some interesting restaurants along the canal.
At Isthmia you'll find a small museum run by the University of Chicago. The site includes an old stadium right next to the Temple dedicated to Poseidon. Look closely and you'll see an interesting starting mechanism that used cords to allow the official to control the start of the race. Archaeologists on the site told me it didn't work, the stadium was later rebuilt with a new starting mechanism. [For more, read the Isthmia excavations report from the Ohio State Website, and an interesting article on the Isthmia panhellenic festivals. If you are passionate about the Panhellenic games, you'll want to read a fine article by Elizabeth R. Gebhard called The Evolution of a Pan-Hellenic Sanctuary: From Archaeology towards History at Isthmia]
The Museum at Isthmia is open Tuesday through Sunday 08:30-15:00
The Sanctuary of Zeus at Nemea evolved with the institution of the Panhellenic Nemean Games in the 6th century B.C. The stadium at Nemea was in use between 330 b.c. and 271 b.c. after which it was abandoned and used for herding. The running surface consisted of 600 feet of hard packed clay. Distance along the track was marked every 100 feet by a small stone marker. Around the edges of the track a stone channel carried water to the athletes and spectators from a small spring. The starting line was a line of stones with toe grooves.
The interesting thing about Nemea is that you might be able participate in a recreation of the games every four years after 1996, thanks to the Society for the Revival for the Nemean Games [read more or register]. It appears there hasn't been a revival for the last few cycles, however.
The small village near the site is officially known as Archaia Nemea--if you are taking a bus to Nemea you'd best tell the driver you want to get off here. The museum is open Tuesday through Sunday from 8:30 a.m. to 3:00 p.m., but hours are subject to change. It is recommended to call ahead: 0746-22739.
A map of the Ancient Sites of the Panhellenic Games
For a map like the one in the upper right, but big enough to see and use, see our Map of the Ancient Panhellenic Games Sites.