Crete or Mykonos

Crete is a bigger island, and while hiking and beaches are certainly among its attractions, the 2 biggest cities, Iraklio and Hania, both offer interesting and historical places to for many days. The archaeological museum in Iraklio, highlighting the ancient Minoan society and finds from the Knossos site just south of town, is truly amazing. It’s a bigger city, and seems a more modern atmosphere. Hania has the old Venetian Port area, with views out to sea last gge lighthouse, and winding lanes to explore. Flight cancellations weren’t any concern, but this was 5 years ago.

I haven’t been to Mykonos, but I understand it’s a big Partying destination, with a big beach-going appeal. Maybe not what you’d prefer.

Which island would be best when we don't want to rent a car, don't
hike, not looking for beaches. We just want to enjoy the views, take
our time and walk around the town but the same streets everyday.

In my humble opinion and with these preferences, I do not recommend the Greek islands.
In fact all your criteria encourage you to avoid the Greek islands
Why not choose a cool European city with streets to walk around every day?

I would look to the mainland. Nafplio in the Peloponnese is considered of the most picturesque smaller coastal cities in all of Greece. Lots to see and do both in town and around the countryside. It would make a lovely base to experience Greece. Otherwise I would choose Crete and look to either Chania in the west or Aghios Nikolaos ( my favorite) in the east.

I also recommend Nafplio as it's close to Athens and you can take the bus to it.

Lovely Old Town on the water and very good bus service to near by world class archeological/historic sites.

Perfect for a 6 day stay

https://www.visitnafplio.com/

Totally agree with Tommy! Nafplio is just 2.5 hours on a modern reserved-seat comfortable a/c bus (get seats on LEFT side for a sea view much of the way). Nafplio considered THE most beautiful Old Town in all of Greece, and since it's on tip of peninsula, surrounded by sea, it can feel like an island. The sunsets from the canopied cafes along the seafront IMHO outdo any island sundowns. Please click every link on that marvelous website.. it will give you EXACT info on how to get there on bus plus SO Many ideas of walks & discoveries. Here are some photos, by a RS top contributor and ACE photog "stanbr", of what you'll see just strolling around https://www.flickr.com/photos/visitnafplio/sets/72157626483407223/ If u r lucky, you may be able to book rooms at the BEST located (and surprisingly moderate price) hotel right on seafront, Hotel Agamemnonon, another lovely boutique place Omorfo Poli.

Chania, Crete is lovely. We spent two weeks there and explored western Crete.
We have been to Mykonos and did not find any party scenes when we were there. Much preferred it to Santorini.
For a full seven days, Chania or Nafplion on the Peloponneasean Peninsula would both be good choices.
Our Greek friends call Chania and Nafplion the two most beautiful towns in Greece.