Greece with a fear of heights

What is your plan so far, and how many days do you have?
I am just not sure how a random assortment of places will help your plan, but I'd say avoid Kardamyli--that drive had me clutching the grab handle of the passenger seat.
I do empathize! I didn't think I had this problem too bad, but at the Cliffs of Moher in Ireland I literally could not walk along the trail. I had no problem in Greece, but I was not the one behind the wheel. I do think you'd probably be okay driving to Nafplio if that is in your plans.

Thanks for the feedback. I have no plans so far. Greece is one of those places that has so much to offer that it is hard to know where to begin (and it will be our first time visiting). I would greatly appreciate any advice. I really dislike feeling rushed so I was hoping to make it a month-long trip, but that will depend on how costly it ends up being. I have not travelled internationally since 2007, so I do not have much of a sense for how pricey things are at the moment. In terms of interests, I like walkable places with nice beaches. I would also be interested in soaking up as much culture as possible. For instance, my daughter loves dancing, so maybe a Greek folk dance workshop? Traditional music concerts, theater, or cooking classes all sound interesting. I would rather see lesser-known places of historical interest that have smaller crowds, especially if her school schedule dictates that we be there during peak season.

Meteora sounds like it's probably a good place to put on your list of spots to avoid.

I recall some harrowing roads going by bus from Nafplio to Olympia, and then Delphi to the Meteora, but that was 20 years ago and both routes could be avoided. The area around historical Sparta is also mountainous. But other than that, most tourist areas should be no issue, especially the islands..

A month -- how lucky! (I am so jealous, lol)
In that case, I would just start planning an itinerary, then post it and get detailed feedback on how to accommodate your fear (totally legitimate) as there are almost always alternatives. I think if you make the dream plan first, it will be easy for people to see what you gravitate to and suggest tweaks, whether they be transportation differences or different locations entirely.
I found the Bradt Guides most helpful, but any guide will give you one month itineraries that you can target to your own likes.

You could start with Matt Barrett's Greek Travel: https://www.greektravel.com

I also suffer with fear of height But I did not have problems in Greece. We visited Crete, Mykonos, Paros, Santorini, and a good portion of the Peloponnesean Peninsula.
Another fan here of Matt Barrett’s Greek Travel.

I would start by doing research on websites to get an idea of what you are looking for.

Greece has a lot to offer and it would be difficult to recommend something.

You need to find an area or areas that may be what you are looking for whether the islands or the mainland then come back and ask advice on those areas.

Driving in Greece is not dangerous unless you drive dangerously just like anywhere else.

Most of it is easy albeit if you drive in the mountains it will be slow going not because the roads are bad but due to the terrain. The coastlines are lovely but very curving and then there is driving through villages which can be an adventure.

Most people fear what they don't know but once you do it you realize it wasn't as bad as you thought.

I also agree that Matt's website is one of the better ones and it's very comprehensive.