If you go to Cape Sounion tomorrow, the weather forecast predicts clear skies.
Bus travel time depends on traffic, but it averages about 2 hours from the departure point in Athens.
how long do you budget for the monastery? Perhaps we can go there
first, then Lavrio, and then Sounion for the sunset at Poseidon.
The Byzantine Monastery of Kaisariani is a 25-minute drive from Athens city center, it's located on Mount Hymettus in a wooded area overlooking the city. Like all monasteries, it is a peaceful spot where you can go jogging or take walks.
It's open from 8:30 am to 3:30 am (closed on Tuesdays). Admission is around €5, and it is rarely crowded. There are small parking areas along the road, from there it's just a short walk along an easy path. The route from Athens city center is very straightforward and takes you through quiet streets with little traffic. Here is a description of the monastery. If you have a car for the morning, it is well worth the trip. You can easily spend an hour at the monastery and explore the surrounding area, there are spots offering beautiful views of Athens and the entire region.
https://www.sofiaskaleidoscope.com/journal/kaisariani-monastery/
Afterward, you can choose to drive along the coast or take an inland route to reach Lavrio. The port of Lavrio, Greece's third-largest ferries port, is just a few minutes from Cape Sounion. It offers plenty of restaurants and tavernas, a Mineralogical Museum (if that interests you), and the archaeological site of Thorikos, located just outside the town.
https://theathenianriviera.com/things-to-do-and-see-in-lavrio/
If, like us, you aren't particularly fond of organized tours, renting a car when you compare the cost of a rental car (plus fuel) against the price of round-trip bus tickets, is a great option that gives you the freedom to set your own schedule and travel at your own pace.
The main challenge is finding a rental agency that allows for a late-evening drop-off (there will be an extra fee) or finding a parking spot so you can return the car the next morning. My "usual" rental agency in Athens closes at 9 PM, but there are others that apparently allow late-evening returns (you'd need to check with them) such as this one located on Syggrou Avenue:
https://avenuecar.gr/