Izmir is FAAAARRRRR better than Adana. No comparison. I have lived in both places.
I don't mean to slam Adana, but it is farther east and the people are more "traditional." The population and traffic can get rather overwhelming. It is also a lot hotter in the summers. Much fewer people speak English there.
Izmir is kind of like the Turkish San Diego, maybe a little New Orleans thrown in. It has much more European and Greek influence (as do the people in Izmir), a beautiful park along the bay, great cafes to sit and watch people go by, far better night life. Excellent white-sand beaches are available around Cesme, at the end of the peninsula, that's less than an hour's drive. The traffic can get heavy, but nowhere near as bad as Adana. The best place to live in Izmir, in my opinion, is Alsancak.
Most people who are stationed at Incirlik Air Base, near Adana, when they go to Izmir they wished they had gotten orders for Izmir instead.
Anyway no question, Izmir is better. To answer your other questions:
1. You can't access any military facilities in Adana. The base is not open to retirees at all. It is a Turkish base with an American presence, and the Turks decide who gets in. In Izmir, you can't use the commissary or BX. You can get in to the other facilities, like the club. This has to do with the status of forces agreement.
2. The expat community in Adana is nil, as far as I know. Unfortunately it's about the same in Izmir. I am sure there are far more expats in Izmir, but there are no places they gather or activities. It used to have a thriving expat community, and we would meet up a few times a week at Eko Pub. But the last time I was there I saw an old-timer expat who said I was the first native English speaker he had seen in a week.
3. Adana has some places along the river where you can run. I don't recall seeing any other places like that, you would have to run on the sidewalk and across intersections. Izmir has some fantastic places. A long path specifically designed for running down the side of the bay in Alsancak, also there is a long promenade around Konak. Both have ample length for long runs.
4. I don't know how I would compare the safety because I don't know the statistics. From my impression, people in Adana are more aggressive in the way they drive than those from Izmir. I recall hearing about more violent crime in Adana, but it was usually between Turks over arguments or things like that. As just a gut reaction, I would feel safer in Izmir.
5. Adana has a few good restaurants, mostly all Turkish food. But Izmir far outdoes Adana in that department too. For shopping, Izmir wins again. The same things are available but there are more malls and shopping opportunities in Izmir. Izmir has more cultural events from what I could tell.
6. I think an apartment would be cheaper in Adana than Izmir, but I'm not sure. Have a look at the
Renting forum and go to some of the online classifieds in both cities and you can compare.
Unfortunately I don't know any real estate agents in either place. But if you're renting, it doesn't really matter. They just show you what apartments are available. They take a commission of one month's rent if you rent a place. Have a look at the Renting forum for more tips on how to find a place. What I do is print out all of the advertisements of places I like, and go to one of the real estate agents who is advertising. I ask them if they will also show me the other places. They will, but they have to split the commission with the other agent involved. So they may try to show you something else that you don't want simply because they are listing it, but if you stand up to that they will relent and show you the ones you really want to rent.