Location Add On to Istanbul

I would choose Cappadocia.
You can bookend time in Istanbul with a flight there and back, allowing you to stay in two areas of Istanbul, or you can fly to the region on arrival and then come back to Istanbul to have all of your time there consecutive.
https://www.captivatingcappadocia.com/cappadocia-airport-which-one-fly-into/

Is this for a group or ?

Why not add Bulgaria?

It’s close, not a major tourist destination.

I had thought of Bulgaria but don't know much about it- will have to research!

Yes, this is for a college program.

Lots to see in Cappadocia. It's far from Istanbul but very worth it imo

What about Izmir? You could visit Ephesus and the fantastic ruins there

Ten days isn't long enough to cover Istanbul plus another country. Istanbul is huge, and getting from place to place takes time. This is my Day 6, and I have so far stuck to walking around the old town, but preliminary checking of public transit routes turned up several situations where connections involved walking a few blocks (not an issue) and locating the second bus stop or Metro station (could be time-consuming). Upon arrival I ended up taking a long bus trip into the city and then a taxi (something I never do), because starting the trip by Metro (which now serves the newer airport) looked like it would require Metro-Metro-Metro-tram, and neither of the Metro connections seemed to be easy.

You shouldn't drink the tap water or use it to brush your teeth, which means sourcing large bottles of water every couple of days. It's sold everywhere, and cheaply, but it's just one more little thing that makes travel less than efficient.

Basically, a list of Istanbul sightseeing goals that looks like it could be accomplished in 4 days/5 nights will take at least a day longer. I'd want to stick to Turkey or at most add a single non-Turkish city--and I think it would be a shame to see only Athens in Greece or only Sofia in Bulgaria. In choosing another Turkish city to include, consider how long it will take to get back out to the airport (traffic can be horrible, at least to IST) and whether you can fly between the US and the other destination rather than having to deal with IST 4 times in 10 days (eek).

I really have no guidance to offer on other parts of Turkey beyond this: I've heard Izmit and Bursa are nice, and they do not require flights. I'm sure a place like Konya or Cappadoccia would contribute to a more varied trip, however.

Honestly, I don't think 10 days in Istanbul would be too long. You could spend a day doing the Bosphorus, hopping off at each stop to walk around, and another day on the Princes' Islands. There are also sights on both sides of the Golden Horn

On a short trip, I think it's worth considering the ease or difficulty of transportation between the airport(s) and the location of your hotel in Istanbul. An area reachable via one simple Metro connection would be great. Staying in the area I'm in, near Sirkeci Station, would be a culture shock, though very convenient for walking to Hagia Sophia, the Blue Mosque, Topkapi Palace and the Archaeological Museum.

For college students, I would choose another location in Turkey, rather than going to a 2nd country. As you say, to immerse in that culture, and also to see the variety of destinations within it.

With 10 total days, I would spend the better part of a week in Istanbul and choose 1 from:

Cappadocia - stunning fairy chimney rock formations and possible balloon ride

Ephesus - fabulous historical site

Antalya - seaside destination with boat/swim options

You could reduce the time in Istanbul and then choose 2 other locations, but the increased transit begins to eat into your sightseeing time.

A logical choice would be Selcuk for a couple of days. From there you can go to Ephesus and see the ruins-highly recommend finding a guide there. Selcuk is a smaller agriculture town that is a nice contrast from big city Istanbul. We flew from Istanbul to Izmir then took the bus to Selcuk.

The ruins at Ephesus are indeed beautiful and well worth seeing, but after a day, there is not much left. Selcuk is a nice town, which is where I stayed when visiting Ephesus, but has nothing really outstanding. If you want a second destination, I would vote for Cappadocia. It has an incredibly diverse landscape that will be like nothing they have seen before, and you could easily spend 2-3 full days there seeing the fairy chimneys, rock formations, and underground cities. But the beauty of Cappadocia is its history and landscapes; not necessarily the culture so much, although there are opportunities. I stayed in Goreme, and one day walked to Çavuşin, a tiny village about 6 km away. Here's a brief bit from my travel journal from back then to give you an idea of what I saw:

As I walked through the narrow cobbled streets I began to see evidence of a long-ago culture. To my left was an older woman with a young girl sitting on top of a load of straw in a wooden cart that was being led by a donkey. Farther down the road I saw a woman leading a goat down the street. The woman wore a white translucent scarf that was wound around her head and decorated with colored trim. Her blouse was a red print and was topped with a multi-colored vest and the bottoms were Turkish divided pants (salvar). On top of that, she had placed a wide-brimmed hat. I continued to see this same type of costume over and over on the women of this village and throughout the region.

On one corner, two older women were sitting side by side and let me take their photo, giggling madly when I snapped it. When I tried to speak Turkish to them, one of them (she was about 4’10”) reached up and pinched my cheek and laughed at me. They all looked like they had stepped right out of a book of ethnic folk costumes. I continued walking through the town, and gained a companion at one point. A little dog appeared from nowhere and scampered around my feet as I walked, occasionally leaving me to investigate something interesting off to the side.

The villagers used to live in the caves above the town but as erosion began to cause problems, they moved into houses below. I was trying to find a way to get up into the caves but was having a hard time locating a path. Luck was with me, however – a German tour group began winding their way up a path I had missed so I quickly got in line behind them. We all huffed and puffed our way up into the hills. At some point near the top I saw them head off around the corner towards an old church and decided to let them go. At this point, I realized it was me and me alone sitting on top of the world with a view for miles around. All around me were magical fairy chimneys and caves dating back thousands of years, and hills covered with bright yellow wild flowers and poppies. The only sounds I could hear were birds and tiny insects – no planes, trains or roaring cars. The peace and serenity hit me like a ton of bricks and I sat back against the hills and stared around me at this beauty.

That said, Istanbul will certainly give you enough culture without traveling anywhere else. I spend 8 days there a while ago and could easily have spent longer. There is much to see regarding the Turkish culture, and an amazing number of incredibly beautiful sights. The Grand Bazaar and the Spice Market could easily take you 2 days to see. Balat is a historic neighborhood known for its colorful houses and winding streets. Your students could easily see a bit of traditional Turkish life here. And Kadiköy is a vibrant neighborhood on the Asian side of Istanbul. It's a great place to experience the local culture.