AMsterdam is just around the corner from me (in US terms) so don't fail to contact me for meeting up.
Lots of good suggestions above. Much depends on how much time you have and what you like. There's the flower beds between Leiden and Amsterdam which are just in season around the time you hope to be here.
Biking is highly recommended both in Copenhagen and Amsterdam and as long as it's dry it's well doable in late April early May