Rick does not cover Corinth, or Korinthias in Greek transliteration. There appears to be these 3 sites: The Corinth canal, the town of Korinthias, and Ancient Corinth. Isthmos, or Isthmia in English, is 4.6-4.7 miles southeast of Corinth. There may be an archaeological site at Isthmia, where the Isthmian games were held and where there is the Temple of Isthmia that was for the god Poseidon.
Rome2rio.com is a good site which suggests that there is a bus route from Athens to Isthmos.
I am having difficulty finding other information on bus routs. For the buses in greece, I discovered a pattern. look up Http://www.Ktel after the ktel part, type the transliteration of the greek name of one of the regional units of Greece. then .gr
for example www.ktelargolidas.gr
A bus trip to the Corinth area you are thinking of, if such a bus trip exists, would cost around the equivalent of 8-20 US dollars. A rental car probably costs at least $60 per day. A chartered bus group day trip could cost up to equivalent of 150 or 200 US dollars??
If there is a guided tour that goes to Corinth and/or Isthmia round trip from Athens, on a charted tour bus, this would seem to me to be objectively or logistically easiest, followed by renting a car, the KTEL buses seeming the most difficult. I have never been to Greece, I don’t know what I will do. I am going to Greece in October. I think I will take the bus from Athens to Nafplio, sleep in Nafplio for two or more nights, and take buses to Mycenae, Corinth and/or Isthmia, an possibly other sites. I have a copy of the Rough Guide to Greece from 2012 that I borrowed from the lobrary; pages 126-127 has a good map of the peloponesse showing archaeological sites at Corinth south of the canal, Mycenae, Tiryns, Agive Heraion, Epidaurus, Nemia, where the nemian games were held, and other sites. There is not time to see everything.