As everyone has noted, cardamom is unique, but depending on the type of cookie, would ground ginger work as a different flavor?

I would use freshly ground coriander with just the tiniest whisper of ground cloves. It won't taste like cardamom, but it will be interesting, and a bit off the beaten track. ;o)

I would open the jars of all my sweet spices and decide by what smells right. Nothing will duplicate the taste of cardamom (we all agree on that!), but I think adding the lemon zest will give something like the tweak of cardamom that none of the others have. I would try mace or nutmeg first.

Yes, nothing really compares to the taste and aroma of cardamom. Depending upon what kind of cookie you are making, I might choose cinnamon as an alternative flavor. Different, but also delicious.

You can try cinnamon instead -- it won't have the same flavor, but you'll get those notes of floral-y spice that you're looking for.

Sadly, nothing can quite replace the sharp floral taste of cardamom. You might try adding a combination of cinnamon and lemon zest to approximate its flavors!

What kind of cookies? What are the other flavorings you are using?