This trip would be best if you rented your own car for the out-of-Athens driving (read what to expect when driving in Greece, and when driving in Athens). This way you are not dependent on bus schedules that might offer inconvenient times of arrival and departure.
In Athens stay at a hotel near the center or in Plaka/Monastiraki areas. In the last five years the center of Athens has become much grittier than a decade ago, but you should still be able to find a good hotel near a metro station so you can easily move around without driving. In Delphi, there are plenty of decent hotels in Delphi village which is within walking distance from the archaeological site and museum.
On your way to Olympia via the Rio-Antirio bridge, you can stop in Covielo beach (a pebble beach hidden underneath the large restaurant off the side of the road) or a little farther down the road in the picturesque town of Nafpaktos. Ancient Greece buffs will remember that Nafpaktos was a very important Athenian ally port and the location of an important naval battle won by the Athenians against the Spartan superior forces during the Peloponnesian War in the 5thc. BCE. In more recent history (yes, 1571 is "recent" for Greece) the naval battle of Lepanto put a stop to the Ottoman dreams for domination of the Mediterranean.
There are plenty of restaurants and a large pebble beach in Nafpaktos where you can eat and swim in the sea. Olympia has more hotels than visitors so you should have no problems finding a bed even if you arrive without reservations. The Archaeological site and the museum are excellent and you can spent half a day visiting both, and if you want to squeeze a little sea side relaxation, you can drive to the nice beach of Kaifas about half hour away.
To reach Nafplion from Olympia, if you are not comfortable driving, choose the road that takes you through Patra and Korinthos. Not that it's any safer than one that goes through Tripoli, but it would be a little wider, and faster. The Olympia-Tripoli-Nafplio road is a lot more spectacular and challenging at the same time. It might be the same distance on a map, but you would almost doubleing your travel time if you go that route. You can spend a couple of days in the pleasant city of Nafplion. It's possible to visit both Mycenae and Epidaurus on the same day, but it would be more comfortable to split the visits in two days. In Nafplio you can visit the castle called "Palamidi" at the top of the hill, walk through its beautiful streets and promenande, spend some time in the lively square (it looks dead before 11pm, but it's hopping with activity afterwards) or swim at the beach behind Xenias hotel. You can also visit the tourist resort of Tolo about half-hour away.
If you are a real ancient Greece enthusiast, it would be easy to visit the excellent Nafplion Archaeological Museum (right on the main square), the ruins at Tyrins (should not take you more than half hour to go throught), and Argos. But you should not neglect visiting Epidaurus. Leave Nafplio for Epidauros early in the morning so you can get there before the tour busses from Athens arrive. Epidauros is worth visiting just for the ancient Theatre alone, but there is an extensive archaeological site, the Asclepios Sanctuary that's all around it. The ruins of the sanctuary and the small museum can be visited in about half hour, and you should spend at least twenty minutes taking in the ancient theatre. From there, you can choose to drive back to Athens by backtracking and taking the highway near Argos, or you can take the northern coast road to Corinth and Athens. Both roads are comfortable to drive on.
In this itenarary I saved the three days at Athens for the end, but of course, you can change the itenerary to suit your own needs. But if you are interested in Ancient Greece, Athens would demand at least four days to visit The Acropolis and it's museum, the National Archaeological Museum, the Agora, Kerameikos and its Museum, and Sounio. If you want to substitute one days in Athens for another day somewhere else (like a day in Korinth), you can skip Sounio since itself would demand a half-day trip from the center of Athens.