Greece has become exceedingly popular, so if you want to have a specific type and standard of accommodation you need to book ahead…..sometimes as far as a year in advance for “rooms with a view”. However new hotels and airbnb are springing up everywhere to meet the demand. Also one used to be able to get off a ferry and be greeted by people offering rooms. This is probably still possible, but to a lesser degree. One thing to remember is «φιλότιμο»…….a Greek will never leave you stranded. Hospitality is an honor that they take quite seriously.
I would definitely make advance accommodation reservations in Athens (for your arrival and departure) and in the summer months, for any particularly “hot” tourist spots like Mykonos and Santorini. You’ll have more flexibility if you visit villages in the larger islands like Crete; the smaller islands like Paxos are usually fully-booked in July, August, and September.
Btw, the same thing applies to rental cars. If you want to explore outlying areas not readily accessible by public transportation, it’s best to book a car in advance in the cities and high-traffic tourist areas. Rental cars were not as plentiful after the COVID pandemic ‘though that might have been remedied since I last visited in 2021.
I appreciate your wish to “wander” and while it might be a little more challenging today, I cannot think of a better, safer, and more welcoming country in which to do this! Hope this helps.