The best times to visit Corinth are spring (April to June) and autumn (September to October). Temperatures are comfortable, the archaeological site is not overwhelmed with tour groups, and the light — especially in the late afternoon — is excellent for both photography and walking.
July and August are hot, busy, and should be avoided for archaeological site visits unless you go early (the site opens at 8 am) and are out by midday. Winter is mild by northern European standards but the light is flat and days short; the site is open year-round but tour infrastructure is reduced. The Epidaurus theatre festival runs in July and August, which makes summer a reasonable time to be in the region even if the heat is uncomfortable at the ruins.