IF you take a car for the Nafplo trip (a smart move, since you only have 8 - 9 days) another worthwhile stop for ancient-history buffs is ANCIENT NEMEA ... a wonderfully executed "sacred Games Site" (runer-up to Olympia).. just 5 mi off the big hiighway. A stunning stadium, with ancient racing-blocks in place .
Here's a handy online map for browsing, buch clearer than Google, shows terrain:
https://euro-map.com/karty-grecii/peloponnes/podrobnaya-turisticheskaya-karta-peloponnesa.jpg NOTE: shows entire road from ATH area -- cllick & it gets huuuge: use side-slides to navigate
With your limited time, for your ancient-site ambitions, I would suggest the following based on experience, going solo using busses, and going in car, with others:
• AVOID Day tour to Delphi! 3+ hours each way, V short time in ruins, 10 busses arrive at once, jampacked museum, tours drag you away for group meal (u pay) & souvenir shops. INSTEAD rent car 11-ish day 3, (u can metro to airport to rent, avoid city driving) Arrrive 2, busses leavng, enjoy museum & site, sunset dinner, stay in hotel (ask West room for view down mountain to sea).
• After breakfast Day 4, backtrack down Mts to Road fork at Elefsina (see MAP) Turn RIGHT (West) toward Pelops. OPTION: at Isthmus, u can hop off for quick walk on Old Bridge to see Corinth Canal (not visible from biggie hiway).. or do this on return trip
• 15 mi into Pelops on Big road, Ancient NEMEA just off highway on right,.. can be enjoyed in an hour. Nemea is Red-Wine Country, local village has tiny bottling-plant tasting room right on Main St!
• Drive back to highway & underpass leads direct to (red) road to NAFPLIO, pleasant 30-min drive thru citrus orchards, olive groves In Nafplio, a white concrete "apron" at seaside is free-parking. Find your hotel & start enjoying Nafplio w walk thru Old Town.
• Next 2-3 days -- Ancient sites, beaches etc. This superb Website http://www.visitnafplio.com/ - tells ALL you need -- beaches, walks where to stay, eat etc - click every link!! NOTE: go MYCENAE,at 8 am, before tour crowds. also TIRYNS, right on highway -- NO crowds, Huge-Boulder construction. For swims, Tolo is OK, but I prefer tiny cove next to ancient ASINE (see map). Also, Great walk around base of Peninsula point, to Arvanita, cute town beach
• To avoid backtracking for site-seeing, do ANCIENT EPIDAURUS yur last AM in NAFPLIO ... check out, drive EAST across Pelops "thumb" (see map). Afterwards, drive to seashore for lunch &?dip? Drive up shore road to ISTHMUS, hop on Hiway to ATHENS.
NOTE: if you want the classic Greece Ferry experience, at end of stay consider day-trip to AEGINA (EGINA) Island. 30-min Metro to Pireaus, get OPEN-DECK ferry (1 hour) to this island, it's like a "mini-cruise"... sit out & view cruisers, freighters, speedboats, 3-masted schooners etc! Aegina has THE most perfectly-preserved Ancient Temple of ANY greek Isle. You can reach it via bus, or car rental or e-bikes (very easy). From temple, downhill path to Ag Marina, a swim & lunch, then bus/bike back to port. THis photo-album shows this lovely trip in Spring - https://www.flickr.com/photos/36264706@N03/sets/72157621604646139/detail/ -- I did this without car & stayed over a night, Aegina very greek population, commutes daily to ATHENS for work ... Note: best to go on a weekday... on weekends throngs of Athenians fill ferries & beaches.