Amtrak is riddled by budget cuts and is in a state of disrepare, so you might get some delays on the way. I took Amtrak from Niagra Falls to NYC and after the 2 hours at customs it was not too bad. There was a point in the trip outside of NYC where they switched the Engine from diesel to electric because the do not allow diesel in Grand Central Stn or something like that. The staff was ok, not great or anything, really about average I guess...The snack car was kinda pricey if I do remember some stuff with ya on the train. We arrived 3 1/2 hours late to NYC.
As for Miami stuff to do...I would guess the biggest thing down that way is the beach??? You could also check out Biscayne National Park.
For some water sports, ie diving, snokling and what not. I have always wanted to go for one of those airboat rides in the swamps.
You will get to see some wicked Cuban flare down thatway my friend!!!! I beleive that Florida had the largest Cuban population in the US
Just some thoughts!!! Have a great trip!!!