Have you been to Greece before? Or other European cities?
How do you plan to move about? Public bus/train? Metro? Rent a car? Uber? Taxis? Guided tours about the country? Local guides for specific spots?
Sometimes I start with
www.tripadvisor.com, looking up "Things To Do" in the cities I plan to visit. Sometimes I just go to the local library and bring back an armload of guide books.
Sometimes I find the country specific forum on this site and browse.
Until you have decided upon the cities you wish to visit, you can't check to see if they have points hotels you can use. I tend to use bidding via Priceline quite often. And Airbnb.
You need some sort of general traveling plan. This is just one, copied from a package tour company, but you could use it as a starting point and adjust for your personal desires.
DAY 1 Arrive in Athens, Greece (Athens is your most likely arrival point.)
Check into your hotel. Start exploring the Greek capital when you've partially recovered from the flight.
DAY 2 Athens
A day to discover Athens at leisure, visiting one of the museums or strolling through the Plaka district
DAY 3 Athens–Corinth–Epidaurus–Nauplia
A walking tour of Athens, featuring the highlights of this ancient capital with a visit to the ACROPOLIS. Next, cross the CORINTH CANAL and journey into the Argolis to stop in EPIDAURUS, located in the hilly countryside dotted with pine trees and oleanders. In this magnificent setting, visit the ancient OPEN-AIR THEATER that can still seat 14,000 spectators. Head for the coast to Nauplia.
DAY 4 Nauplia–Mycenae–Sparta
This morning, enjoy an excursion to the ARCHAEOLOGICAL SITE and the MUSEUM OF MYCENAE, a city fortress cursed by the gods but rich in gold and warrior kings. Travel deep into the Peloponnese to Sparta, where history hangs between reality and legend.
DAY 5 Sparta–Mystra–Olympia
Enjoy sightseeing of the medieval BYZANTINE CITADEL OF MYSTRA, at one time known as the “Florence of the East.” Continue to Olympia.
DAY 6 Olympia–Patras–Delphi
Focus on Olympia, where the athletes of antiquity performed in honor of the king of deities. Learn more about the history of the Olympic Games on the optional sightseeing tour. Later, travel north to Patras, the capital of the Peloponnese and the west coast’s largest port. Then, via the spectacular RION-ANTIRION BRIDGE through the picturesque fishing villages along the south coast of the mainland to mystical Delphi.
DAY 7 Delphi–Kalambaka
Sightseeing of the archaeological site in Delphi. Once called the “Navel of the Earth,” Delphi was the greatest oracle of the ancient world, where people flocked to seek advice. Now, it’s one of the grandest sites in Greece. On to Kalambaka.
DAY 8 Kalambaka–Meteora–Athens
A short drive to Meteora, a cluster of spectacular Christian-Orthodox MONASTIC BUILDINGS perched in an unforgettable manner on a set of rising rock formations. They were originally built by hermit monks living in caves carved into the rocks. Later, drive south to Athens. Have a Greek dinner.
DAY 9 Athens
A full day to explore the unseen parts of the city, do last-minute shopping, or maybe even join a local guide for a walking tour.
DAY 10 Athens