Yeah, book your accommodation ASAP, especially for Miami Beach. Like someone mentioned, that's getting into Spring Break season, when Miami gets invaded by college kids. This may or may not be a bad thing, depending on your tastes.
Also, NYC in March might still be a bit cold and grim, so I wouldn't spend too long there.
13 days is actually a fairly long time. I'd maybe split it up like:
* 5 days in NYC (gives you time to do a day trip to Niagara);
* 1 day's travel time;
* 5 days in Miami;
* 2 days in Key West.
You've probably got a pretty good grip on NYC already, but let me give you some tips for Miami:
1) Stay on Miami Beach. Specifically, stay on Ocean Drive. Specifically specifically, stay anywhere on Ocean Drive south of Fifth, or north of about Tenth and south of Lincoln Road.
If you're going to Miami Beach, it makes sense to stay on Miami Beach, and Ocean Drive is
the iconic stretch of Miami Beach—it's got the gorgeous Art Deco low-rise hotels, the beach bars, the palm trees, you name it. South of Fifth is quiet and residential; Fifth to Tenth is a horrible mess of noisy tourist bars (though it's fun to visit!); north of Tenth is very classy and personally my favorite stretch.
My pick for hotels is either the Winter Garden, or the Royal Palm South Beach. Trust me on this.
2) Do a day in Little Havana. I can't find it right now, but there's a Little Havana food walking tour I've done before: you wander around Calle Ocho, try some sandwiches, cafecitos, etc etc etc, and basically get the flavor of the place.
3) Absolutely do the Art Deco walking tour. It starts from the Miami Design Preservation League at 10th and Ocean Drive; takes about two hours and you'll get a great appreciation for Miami Beach's gorgeous architecture (and how Miami Vice saved the city).
4) You've got long enough that you could do a trip down to Key West, and fly home from there. If you don't want to drive, there are bus services that run all the way down the Keys, over the Overseas Highway... which is one of the most beautiful roads in the country, up there with Utah Route 12 and California Route 1. I mean!
Get a load of this!
Key West is pretty small, and two nights there should be plenty, but it's a fun town, and it's totally worth it. If you like cats, go hang out at Hemingway's house (where there are lots of very cute cats); if you don't, go hang out on Duval Street and chill out in the bars.