I like your idea of swiss or provolone. If it's a little bit of tangy flavor you're looking for, try an aged cheddar. We have two in the fridge at home - one is white and aged 2 years, the other is yellow and aged 3 years.
They're both delicious, but I prefer the 3-years aged variety.
I love good cheddar, best. Good on apple pie, which now has me thinking we should have pie and cheese. Now I am hungry!