The rooftop at the Met opens in April. If it is open when you are there it is the perfect proposal spot overlooking central park! I witnessed a proposal there once and it is just magical. This was last year's exhibit (which was a bit underwhelming compared to the prior two years but lovely setting nonetheless) http://www.metmuseum.org/exhibitions/listings/2011/anthony-caro-on-the-roof..
Sorry...just saw you said early April so the rooftop might not be open. The weather in Early April is unpredictable. Prepare for it to be somewhat chilly (50s), that said we do get the occasional perfect 60-70 degree day at that time.
So fun, yes, as PPs said, prepare for any kind of weather, could be 50s and rainy, could be 70 degrees. So be ready! A proposal in the rain could be equally as amazing as on a sunny day...I would look into sunset spots in NYC as it's not always totally visible. Central Park is always a good bet (though I'm not sure for sunsets), you can row boats at the Central Park Boathouse and propose in the middle of the lake. CP is obviously very famous for engagements.
Another idea, depending on weather (or not!) is to walk to the Hudson River Park. I recommend starting (all the way on the west side of the city, at the hudson river) at around 14th Street or slightly lower. Just start a nice stroll down the park, it goes along the river and the park gets more interesting and beautiful the further you go down. If you look at the HRP website, they'll show you all the neat details and alcoves. There are some beautiful settings, near the Battery is my absolute favorite and you can see the Statue of Liberty from there. Honestly, that is my dream proposal...
Good luck!! NYC can be an incredibly romantic place for a proposal. If you decide to do a dinner afterward (you'll have to eat at some point, right?) I recommend finding a great non-touristy restaurant. (Can recommend if needed) Out of towners can often get caught in the tourist trap missing some of the coziest, romantic places in the city. Best of luck!
I suggest that you let her plan the proposal (unknowingly).... Right before you go say, "I want both of us to have our most perfect days in NYC. So I'll plan one day and you plan the next." On the day that she has planned, pick the place she has been most excited about and do it there. That way you know she wont be expecting it (since she planned it) and that place will be special to her in some way (since she planned it).
Anyway you do it will be special though. Don't stress!