I guess it's all about what your taste buds are used to. For me cardamom and cilantro are staples in my kitchen. I can't cook Indian food without these two key ingredients.
I don't find cardamom weird in cheesecake. I use it in bread puddings, panna cotta (try making it with saffron and cardamom), kulfi (a rich Indian icecream) and rice puddings.
You don't have to bake to try the subtle hints of cardamom. I challenge you to try the rice pudding that I make with cardamom in it and see if you can put it back. Most of my American friends can't get enough of this stuff and some of them never tasted or liked spiced up rice pudding until they tried my version.
If you are interested, send me a Private Message and I'll forward the recipe.
Also cardamom is not very expensive if you know where to buy it. You can get it even shelled in Indian stores in super small packets. I also put ground cardamom in tea and it's amazing.
One of my friends used to make green tea (loose leaf) and seep it in hot water and add freshly ground cardamom and then strain and serve. Amazing stuff.