With things like they are in Turkey now, I think the only one left is Lajes, and a handful of 24-month assignments to Osan that you probably don't qualify for. I think Guam is now a long tour.
UPDATE: Al Udeid also has 24 month accompanied tours, but there are only so many permanent billets there, and only some of those allow for command sponsorship. The info on in myPers.
Check with MPS and talk to your Chief. What it really comes down to is what is available.
I don't think they are allowing any dependents to Incirlik now. You aren't going to get an accompanied tour to Kunsan, and Osan is iffy at best (like I said, I don't know if they even have a 24 month accompanied short tour option--you may have to do three and it would be a long tour).
As for your other question, yes you can do back to back short tours. It's called a COT.
There are varying short tour lengths. Korean assignments are usually 12 months and most others like Thule are too. I think Lajes is 15 months unaccompanied and 24 months accompanied and I think Incirlik is the same (whenever they allow dependents). They made some key billets at Incirlik 24 months regardless of whether or not people were accompanied, and I think there are some key billets in Korea that are the same way.
UPDATE 2: Ok, I just read your latest question. You are not security forces. You are a civilian. Like Goose said, don't get wrapped around the axle. You'll get what you get. Also, forget everything I just said about talking to your chief, the assignment team, going onto myPers.