You can have islands at any height, depending on how you want to use it. Some are lower (30") for rolling out dough and baking...which would be okay for regular chairs. Other islands are a little taller (36") and are the same height as normal cabinets...which usually take stools. Sometimes one side of an island is even higher that the work area (42") to hide some clutter and this takes taller stools.

You can do any type of island you like, but if you're not needing a low island, you could drop the seating area down to 30" for the chairs, but keep the work area at 36".

You'll get even more advice (and probably beautiful pictures for examples) on the kitchen forum. Best of luck with your new home :)

How will you be using the island? I kept mine at one level because I wanted a large space, all the same height, to spread out buffets and for when I need a large space to spread out (like making cookies at Christmas). But if you don't plan to use yours that way, then the lower height for the seating might work. I find the counter-height stools (for 36" counters) comfortable, but I don't like the bar-height stools.

I have 2 young daughters so I thought a low island would be good and therefore no table is needed.

I like your idea about a big island and eliminate the nook. Our counter is 37 3/4"
and we have a stool at 26" (seat). I am 5-4" and like the counter height for sitting or working at. I don't think this is what you are looking for - stools not seats.