Can't recommend much in Brooklyn 'cause I only ever hung out around Park Slope. Brooklyn Heights can be cool to walk around 'cause of the architecture and views of downtown Manhattan. You could try walking across the Brooklyn Bridge to save some train fare...
Definately agree that the West Side of the Park is nicer, but if you're going to Metropolitan it'll be easier just to walk up and down "Museum Mile".
Metropolitan takes at least a day though:
- some cool medieval armor displays
- a nice Japanese room in the Asian Arts wing to sit down and catch your breath
- definately check out the Egyptian tomb(?) that is reconstructed inside the museum; the contrast with the full wall of windows looking out on a green park is nice on the eyes
- good collection in the European wing; easy to spend a day just in there just doing quick drive-bys of the paintings.
- if you're going alone, bring some tunes (not a boombox though, unless you're planning on challenging some of the security guards to a break battle)
Depending on what exhibits they have going, I'd also suggest checking the MoMA and the Whitney Museum. Whitney sometimes has some freaky video art installments. Guggenheim may or may not be worth a visit; if you can smuggle a skateboard in, you can ride it down the circular exhibit walkway...
http://www.whitney.org/welcome.html
http://www.moma.org/
http://www.guggenheim.org/new_york_index.html
If you're interested in tasting some sake again, you can head to Little Tokyo around the East Village/Broadway neighborhood. There's a nice, noisy basement sake bar at 240 E.9TH ST called Decibel there that is good for pre-festivity drinking.
If you want a real NYC beer, you should hit McSorley's Old Ale House in the East Village. Place hasn't been dusted in years. (15 E. 7th)
If you want to shoot some stick, stop by the Stoned Crow in the West Village; tell Betty, the owner, you're a friend of mine and she might buy you a beer...(or she might kick you out)
Been to Ground Zero once, but I can't really say one way or another whether it is a good destination.
I'll probably think of some more places, but give me a holla if you need anything or someone to hook up with there. I miss that town.