Well the acid-base reaction that you did should produce water and NaNO3, as you say. Sodium nitrate is very soluble in water. I'm not sure what you did procedurally after adding the nitric acid, but since nitric acid is an aq. solution, I would have expected the sodium nitrate to dissolve. Thus if you filtered off the water layer or removed the water somehow, I would think that the sodium nitrate went with it. Maybe not, but that's my guess.
Copper nitrate is a bright blue powder (or blue solution if dissolved in water) so as long as you don't see any blue I'm quite sure you don't have copper nitrate. I'm not sure about the nitrates of the other two metals.