It would be a shame to spend only a couple of days in Istanbul. If he is there on business, can you not see some main sites on your own, then do some of the smaller gems with him? (Chora church, antique parts of Grand Bazaar, topkapi palace, etc etc ) with him?
In terms of doable destinations from Istanbul, it depends on your interests and what time of year you are going (weather). Some ideas/thoughts:
Bodrum--gorgeous seaside town, castle/museum and remains of Mausoleum, clubs at night--2-3 days
Ephesus--among the best sites of ruins, esp if you have interest in Greek/Roman and/or early Christianity (remains of Church of St John are there, in addition to main site of Ephesus. Most Can be done in 2 days --add in another one if you book a nice hotel with pool and lounge around)
Antalya: south coast of turkey so takes longer to travel there/back, but fantastic coastline and amazing ruins of Side and Perge
I forgot to mention that you can do day trips (minibus tours) from Bodrum to places like Magnesium and Pergamom.
You can also do a day-long boat trip from Bodrum (also from places around Antalya) where they take you to little gorgeous coves etc. But it all depends on the season, OP. After September the boats/beach time would not be as realistic.
I'm a ruins/museums/seaside person if it wasn't obvious
As for Capadoccia, it has impressive /unique scenery too as well as Goreme, location of renowned Byzantine Rock-cut churches--but they are kind of a niche art history thing so not sure if they would appeal. I found the "underground city" tours very fascinating....im not sure all tours go there but it's well worth looking for one that does. All tours will bring you on the mandatory stop at the alabaster shop/pottery shop, of course! I have never done a balloon tour as I thought it was a bit touristy for my style. I did find the landscape really interesting.