We are 4 people travelling from Athens airport to Chania, Crete. Thinking plane is quickest way to get there. From Chania need help to figure out quickest,cheapest way to get to Naxos. After a few days in Naxos need help to figure out quickest and cheapest way back to Athens. In Naxos will stay in Naxos,Egee . In Athens will stay near Acropolis. Also need recommendations to get from our accomodations to the port or airport you will recommend.

Moved to Europe board

The Sea Jets Company "Champion Jet" departs at 08:40 from Heraklion on Crete to Naxos, stopping at Santorini before reaching Naxos. Book through their website. Get to Heraklion the night before so you don't have to stress about missing the morning ferry.

Note that there is a difference between quickest and cheapest way.
Quickest way: catamarans, seajets, etc. as mentioned above
cheapest way: slow ferries like Rethymonon (twice weekly) or Iraklio (almost daily) - Santorini and Santorini - Naxos

My main concern is the shortest distance, from the towns where am staying, to either get to the port to catch a ferry (max 2.5 hours long), or to take planes with shortest
travel time. I will not be renting cars to get around. Prefer to travel in the morning to benefit as much as possible from sightseeing time.

You might consult rome2rio.com -- just be sure to click through to the underlying links as the main site is not sensitive to seasonal variation in schedules.

Do you plan to stay just around Chania airport (Souda) or would you prefer to go to a really nice place?
For sightseeing, beaches .........?

You don't say when you are travelling, but in summer Champion Jet 2 leaves from Rethymnon on Tuesdays and Saturdays. Not much good to you if you leave for Santorini on another day, but Rethymnon is a lot closer to Chania than Heraklion.