If you want your core to show, then the only way is too cut that body fat. But, you can build muscle around it, which makes it larger, and obviously more prominent.
Squats and deadlifts will be excellent for the core, since you need to recruit it to stabilise your whole body. Aside from that, direct exercise is also good. I'd honestly recommend getting a fitness ball, and doing ab crunches on it. You have to get it into the right position, so that your core is always tense to help stabilise you on it, but also when you crunch, you'll be able to feel the burn. It really makes your abs defined after, and is good for those deeper stabiliser muscles. Otherwise, if you really want to just add mass, do decline crunches with weights. So long as your lower back isn't screwed, you can go really heavy, and just like any other muscle group, your abs will be subject to hypertrophy.
Honestly though, if you really are 'fit everywhere except your core', then it's either, you're not actually fit everywhere, OR your body has a large tendency to store your body fat in the abdominal region. No amount working out your core will help that, at best it may make your abs slightly more visible (since they will be bigger), and thus, it may make your abs feel firmer by virtue of it being less concentrated in fat (since there's more muscle), but the quantity of fat on your abs will remain the same, and that can only be removed through burning fat.