Where can I hide an AC to DC adapter for cove lighting?
I invite other answers, but since you mention cove lighting specifically, there are slim transformers that are made to be easy to hide like this model: 



Armacost 12v LED Driver transformer

To use this, you could have a 120v standard electrical box behind the molding where the NM cable would exit the wall and attach to the transformer.  I'm not sure exactly how to make the transition from the wall to the transformer in a 100% by-the-code way, but the electrical contacts are covered and since it is cove lighting, the connection will be inaccessible to anyone that wanted to touch or snag the wiring.

The transformer would be easy to hide in the "tray" of the molding and comes in different output wattage depending on your needs.  Now, I've never used this model and I'm certainly not trying to advertise it - I'm just pointing it out as an example of the slim-profile transformers that are available.