Many of the islands have international airports, so you can certainly fly directly to your first stop, without a detour and as such bypass Athens completely.
This makes travelling between these far easier as they are usually located closer compared to islands on other groups.
Picking islands that are within short distances of each other, and planning your routes wisely, will keep transportation costs at a minimum.
A ferry from Athens to Santorini for instance would take just under 5 hours on the fastest ferry, compared to just 50 minutes by air.
It’s a good idea to try to visit Greece in October, or between April and June. It’ll still be warm enough to enjoy an island escape.
If you decide on a group of islands to explore, you’ll be able to enjoy your time on each island without rushing. You’ll also spend less on ferry trips.