It kinda depends on what you want to see. I think more stuff would be at peak bloom in early to mid May than late April but things are chuggin along right now. At least in May every tree will have its leaves out and it will really look like Spring has sprung.

NC Botanic Garden in Chapel Hill will look best early - for all the natives but Duke and the JC Raulston Arboretum will look better later for the big perennial borders. If you want to see masses of bulbs then earlier at Duke would be better - but they should still look great in mid May too.