The new Mustang drives far better than any previous one. I actually enjoyed it more than the new M3 and Lexus RC, as I found it more involving.
Among BMWs, I like the 2-Series best currently. But I also tend to prefer compact cars over larger ones. The main thing I have against the Mustang is that it does feel a little large and heavy.
The second issue with the Mustang is that its interior isn't as nice as those of the expensive German cars. I'm okay with most of it anyway, but wish they hadn't molded such obviously fake stitching into the instrument panel.
I haven't yet driven the S3. The A3 isn't nearly as fun to drive as the Mustang or the BMW, but it's handling is safer. I did enjoy driving the GTI, but that said it's a much different feel than the RWD cars.
It's not yet possible to say how reliable the all-new Mustang will be. Previous ones have generally done well in our survey. The BMW and Audi should be reasonably reliable (perhaps even very reliable) for at least the length of the four-year warranty. The 2015 A3 and GTI have been outstanding so far in our survey--but they're still very young. After 4-6 years German cars tend to get expensive--though the latest ones could be better (too soon to say).
Really, you can't go wrong with any of these cars. They are all very good, just in different ways. So it's very much a matter of what sort of car you want.
The only Asian cars that might fit what you're looking for are the Genesis Coupe and Q60 (G37). But neight is a match for the three you've already listed.