First -- when u say daughter interested in Mythology, we don't know whether she's a college student who's taken some course sin classics & archeology, or a 9-year-old who's read "Percy Jackson" and thinks she'll see statues everywhere of Hercules, Ares, and Minerva. For the former, Greece can be the thrill of a lifetime... for the latter -- she must be prepared that nothing is like the fantasy books, and some prep will be needed if she's to appreciate essentially ruins in a beautiful setting.
Next of all, no driving right when you arrive, you will jet-lagged to the max... instead, get ye to a nearby hotel, have a bite to eat & crash. There's a nice hotel right on a beach, about 25 minutes away by FREE shuttle... Avra Hotel in Rafina (the only rule is, you must sign up for free shuttle at same time u book the room, so they can plan). Then return to the airport refreshed, AM of day 2, pick up your rental car and Off you Go! Heres a scenario that can work:
DAY 2 - Pick up car around 9 (athenscarrental.com gets VERY good reviews & I've used it 2x). They bring your car right outside the Airport building, & return to same place (NOTE: you do know tht yu need a Intl Driving Permit to rent -- get it at local AAA in 20 mins). Your drive to Delphi avoids city entirely -- for complete route in advance use https://www.viamichelin.com/ route planner -s hows mapl also step by step PLUS est. time & Cost in petrol &tolls. Takes about 3.5 hours... you'd arrive mid-afternon, when most pesky bus-tour groups are leaving. U might visit museum first (very well signaged), good prep. the Site is open until 8 pm in June usually, and sunset is not until 9, so you actually can see museum & site same day. You have a choice (1) if interested in doing "homework" in advance, u can use good websites to study & print out, & D-I-Y or (2) if u don't want to, & have the €€ there are several excellent licensed guides in Delphi who can meet u onsite... usually 2 hr minimum @ €60 per hour. Your choice. When u arrive, pop into 1 of several hotels right on the main street get room for the night... At Hotel PAN the back rooms have stunnin balcony views down mountain to the sea (we were on the main floor an hawks circled BELOW us). If u time it right u can enjoy a light meal on a terrace right by the same downhill view & sunset. Don't miss the "Athena Tholos" round temple down the road from the main site.... and enjoy Greece's BEST water, right from the tap; it comes straight from snow-melt atop Mt Parnassus.
DAY 3 - Drive back down mountain to Elefsina (at this fork; LEFT goes to Airport and RIGHT goes across Corinth Canal on modern highway toward your ancient landmarks --- NEMEA, MYCENAE, and EPIDAURUS. Here is a good online map -- http://euro-map.com/karty-grecii/peloponnes/podrobnaya-turisticheskaya-karta-peloponnesa.jpg -- click & it gets huuuge, use side-slides to navigate. It makes everything clear. Just after Corinth Canal about 10-15 mi, an exit just on Right takes you to NEMEA "Ancient Games Site" the runner-up to Olympia. Great short stop ruins, temple columns and FAB stadium, where u can run from starting-blocks 2200 years old (in July, athletes from over the world will gather there for the 4th Revived Nemean Games!! https://nemeangames.org Go Under big highway, head South toward Nafplio, great place for a night or 2. If you're up for 2 ancient sights in 1 day, you can turn off this road to Mycenae (MIKINES on map, that's how the Greeks spell it). Here is where advice depends on knowing if daughter is 9 or 19! If you get to Nafplio -- the most Beautiful Old Town in Greece -- you can check into a hotel, take a deep breath & head for a waterside cafe for IMHO the most gorgeous sunset in Greece. Here's a photo album of its beauties (PLUS pix of Nemea, Mycenae, Epidaurus). (Continued On Reply #2)