Santorni and Mykonos by land or by sea?

No contest, by land. Santorini is all about the views of the caldera.

We arrived by sea (ferry) and stayed 3 nights. It was amazing!
Some years earlier I saw it by cruise ship. Had less than a full day. Not even a close call. Go by “land”.

But what if you are visiting by chartered yacht?

Answer to Jimbocha YAcht question -- it depends on the "Yacht". the big 3-masted ones anchor in caldera below the Old Port -- where u need to take the cable-car up... competing with many thousands from cruise ships (as many as 3-4 cruise-monsters may anchor, with up to 10,000 psgrs). Smaller 6-8 psgr vessels are restricted to ports at far south end of Santorini I am told.. friends who chartered one said their skipper wouldn't take them there because any waves at all make it very iffy to moor.

Santorini is so over-touricized/over-promoted Any time between April & late October, a satisfactory visit depends on strategies to avoid the worst of crowding. Difficult to advise when not supplied with key infoo -- just a day trip? 2-3 days? week-day or weekend? Starting from Athens? Where need to be afterwards?

For persons who want to visit before a cruise and who arrive Athens, we usually recommend allowing a 2-hr layover to take 1st available Aegean or Sky Express (50 mins) to Santorini. Tip - Weekends have fewest cruise dockings. I advise staying in Firostephani, just on N. fringe of main town (FIRA), easy walk to attractions but away from throngs.The Main thing is the Famous Caldera View, you can appreciate i short stay. For calendar-famous village OIA, try to bus or taxi super-early 8 or 8:30am to beat the invading cruiise armies... then bus to FIRA & then to other areas. I have visited Santorini numerous times because it's a "must-see" for my newcomer companions... I only allot 36-48 hours, and they are very satisfied, & happy to move on to other destinations.