Greek islands not for museums or archeology but

You can't beat Santorini for most of those requirements - other than the crowds. But it's worth overcoming crowds to see such a unique and beautiful place. In my opinion, there's not a more picturesque place or a more romantic location than a sunset in Oia. The island has great wine, great food, excellent coffee and there's enough to do there to fill up a few days. Crete is also close by but a much bigger island so you could spend a week or more in Crete and the rest of your time in Santorini. I also really like the Ionian islands, specifically Corfu and Kefalonia. These islands are much less crowded and are still beautiful and romantic. Great wine and food are a given anywhere you go in Greece.

Lots of shops, galleries, hotels and restaurants close in October, not to re-open until the following April or May, so your choices might be somewhat limited if you go then, but Naxos and Paros would be good choices because they have fairly large permanent populations so many businesses stay open all year long.