Why enclose space? Is it there for barstools once counters are put in? I'd consider an island... but you may not want to take out that which has been built.

I think white for a basement is still the way to go. As I showed you can add a bold backsplash, white doesn't mean boring. Once you commit to a backsplash color though - you are bound to it. Instead you could paint all the walls in the 'nook' a bold color too. The nice thing about white is that you can add or subtract color as you live in the space - as well as change a look of a room on a whim with accessories and paint. For now you could buy, for example, all red appliances - like a blender for Pina Coladas and even unfinished wooden bar stools you paint red! Get bored with red - grab a paint brush.

What will be on the floor? What's your style? What kind of furniture will be in the rest of the space? Those are all things you have to take into consideration when choosing something fairly permanent as a kitchen colour. I think that making a moodboard, collecting photos you like in your ideabook will give you a good idea of what you'd like and it will narrow down your choices.