Which other city/place in Greece for two nights, if not Athens

Athens is not my favorite place in Greece, so I'm not going to try to convince you to spend the rest of your Greek time there, but have you explored your transportation options? I suspect you'll find it difficult to get to Santorini without going through Athens twice. If so, you won't have much, if any, extra time to spend somewhere else in Greece.

Four days is an extremely short time to spend in Greece because of the logistical challenges you'll face when you try to move around. Your Greek stay is going to amount to a lot travel time and less sightseeing time than you're probably expecting. Are you sure you want to do this? If you run into a flight problem, you could end up with almost no time in Greece at all.

If you are not interested in archeological/historic sites then Athens may not be for you. However, there's more to Athens than "ruins". I would do a lot more research on the city because while it's not Rome it does have some very interesting areas of the city and is worthy of a visit.

Four days is really not enough time to spend. It takes time for ferrys to get to Santorini and return. A flight would be quickest saving lots of time on a boat.

As stated earlier you have to go through Athens to get to Piraeus for ferrys so you may end up in Athens whether you want to or not.

If you want a real nice town that's only 2 hours or so from Athens then head for Nafplio in the Peloponesse. It's one of Greece's prettiest towns, lovely waterfront, beautiful Old Town, historic sites right in town and while you may not be interested in archeology it's a short distance to two world-class archeological sites, Epidavrous and Mycenae. You can also do a day cruise to Hydra/Spetses and get back to Nafplio for night out.

I think that might be a good option. It will save time on getting to/from Santorini, get a feel for a lovely town, excellent tavernas, pleasant walking and a small beach on the back side of the town.

There are not many paths for public transport between Greece and Turkey. Thessaloniki is Greece's second city, not really any more attractive than Athens. Both cities have excellent archeology museums with the good stuff that came out of some of those historic rock piles. You can fly from Santorini and other islands to Thessaloniki and from there to Istanbul on Aegean and Turkish airlines.

Do some research on Thessaloniki and see if it looks interesting to you. I enjoyed a couple of days there quite a few years ago. As Laura said it's pretty easy to fly there from Santorini and then from there to Istanbul.

Nafplio is really nice, but getting between there and Santorini will take time and inevitably take you into or near Athens. Nafplio is on a beautiful bay with a nice waterfront, good walk around a peninsula to the west and south, great pedestrian center, lots of good food and drink, good museum. Above are the ruins of a Venetian fortress, and ruins of another smaller one on an island in the bay, but you don't have to visit either. ;-)

Nowhere in Greece is ruins-free as far as I know. But if you avert your eyes......

The islands of Naxos and Paros are easy stops on the way back from Santorini and they both have frequent and daily ferries to Athens. Easy to stay within walking distance to the port in Paros at hotels across the small road to the waterfront which has some nice tavernas and shops between hotel and center of town/port. Naxos is also lovely. Both have nice beaches and a true Greek island feel.

I would love Athens even without the ruins. That being said, as mentioned about, Napflio is a gorgeous city a few hours drive away. Tolo is a smaller town that's right on the beach and close enough to Napflio that you can drive there easily if you want a larger city. It can be overrun with tourists during the high season, but I still like it. I think Delphi is perfect for a two night stay--there are primarily ruins there (also the UNESCO heritage site Hosios Loukos, the battlefield of Thermopylae about 1.5 hours north, and the memorial to the victims of the Distomo massacre also close by) in the city proper BUT they are lovely and enchanting and a wonderful place just to sit and have a picnic or read even if you don't care about archaeology. The town of Delphi is packed with buses during the day but tends to drastically clear out at night so I love staying there. The only problem is it's a 4 hour drive from Athens roughly so that would be difficult with your short time.

You could just go to Chios, Lesvos, Limnos, or Samos which are right on the way to Turkey and not go to Thira.

Or, find out which islands have direct ferry service from Santorini. Rhodes is one and that's right off the Turkish coast. It's really the only one that is in that direction. Other choices would require a return to Athens. Which may appeal to you, based on your existing travel arrangements.

These are long ferry rides, keep in mind. Each are about 8 hours so if you've got two days for each a huge chunk of that is going to be those long ferries.