Just out of curiosity, where would you, OP, be coming from and is anyone coming with you or joining you?
Should I get some city transit day pass (bus/light rail combo)?
The Metrocard is a magnetic swipe card that's the same for bus or rail (just the NYC subway though, not the commuter rail or PATH train). If you think you're going to be jumping around a lot, then consider getting an unlimited weekly pass (there is no three day pass right now). If you're handy with Google Maps, use it to check if the bus, rail, or walking makes the most sense. There's also a city bikeshare program you can use to bike around, but I recommend this only if you've biked in an urban setting before and/or you are a pretty frequent bike rider.
a) Ferry / boat ride of some sort
The (free) Staten Island Ferry was already mentioned, but there are two low cost ferry options available to you and a lot of more costly options. The two low cost options are
the East River Ferry and the
Rockaway Ferry. These rides are $2.75 each way. Both of these ferries take off from the same pier in the Financial District. The East River Ferry goes to a lot of trendy neighborhoods in Brooklyn and Queens which you might be interested in, though your time is pretty limited. I think this might be sensible if you combined it with a walk across the Brooklyn Bridge where you walk the bridge one direction and then take the ferry for the other direction. The East River ferry's landing in Brooklyn near the Brooklyn Bridge is actually part of a new and very scenic park that has a beautiful view of downtown Manhattan and is a really bustling. One of the great pizzas of the city, in my opinion, is Juliana's which is near the park though the wait can be very long. The Rockaway Ferry goes near some of the city's beaches portions of which are really fun, but I'm not sure if you're aiming to spend time hanging out at the beach with a long boat ride with such a short trip.
b) Maybe one of those bus tour rides?
Sure? I've never done it before.
c) The best authentic NYC pizza joints
Some of the best are too deep into different parts of the city for it to be worth it to go to. For one's that might be in the core of where you're visiting, some of the ones that are accessible and I've liked are Julianna's, Prince Street Pizza, Joe's Pizza in West Village, and Rubirosa. Julianna's is going to be more of a personal pie sit down affair, Prince Street Pizza and Joe's Pizza are classic quick slice joints where you get them by the slice at a counter, and Rubirosa is a sit-down place that serves pizza from Staten Island in the city where the crust is really thin.
d) Place with authentic Philly Cheesesteaks just as good as in Philly. I'm unable to go to Philly this trip.
I would skip Philly Cheesesteaks on this trip altogether. NYC staples that I'd suggest instead are on the next response.
e) Other suggestions of "must-eat" locations while in NYC (suggestions please! Best NYC Hot Dog?)
A great dry-aged steak at a storied old steakhouse that is not a chain (Peter Luger's, Keens, Delmonico's though I'd actually order the seafood instead here, Sparks, etc. but make sure you get a reservation first),
Some random foreign cuisine you've wanted to try but can't where you live or even something that you can't get an authentic version of (very authentic regional Chinese, Japanese and Korean are available within Manhattan, etc.)
halal chicken/lamb and rice carts - these are street carts selling these rice, meat and salad platters with a white sauce and optional red hot sauce. I like the various Rafiqi's carts, but the usual one people say to go to is the Halal Guys cart on the southeast corner of 53rd and 6th near the Museum of Modern Art.
a NYC brunch with eggs benedict or some other silly egg thing with a mimosa
smoked salmon / lox and cream cheese on a bagel possibly with onions or capers or something else from (Russ & Daughters?)
a great pastrami on rye (Katz's Deli or Pastrami Queen if you're in the Upper East Side)
Eating a mind-numbingly just stupid amount of oysters (Grand Central Oyster Bar nets you a visit to Grand Central as well)
f) New World Trade Center
Sure, but this gets really flocked so I'm not sure the time spent on this would be something you want to do
g) Rockefeller Center (NBC studios, observation deck)
This is sort of fun
h) The Met (any other "must-see" museums or the like?
What kind of things are you interested in seeing?
i) Times Square
Try not to eat here or in the general area, because it's overpriced and generally not very good. If you do, the Starlight Diner nearby is at least super kitschy which might be entertaining.
j) Best Shopping District/Mall?
There's not much in malls, but 5th Avenue in Midtown and Soho are the bigger shopping districts. What are you looking to shop for?
k) "Must-see" villages/burrows if I only have limited time and can't see them all (Queens, Brooklyn, Long Island, Coney Island?)
What are you interested in? I think the Brooklyn Bridge walk one way to Brooklyn Heights/DUMBO neighborhood in Brooklyn and then a ferry ride to Financial District the other is a good one. Since you have three days, I'd say it makes sense to stick mostly with Manhattan except for the stretch in Brooklyn Heights/DUMBO unless there's something you're specifically looking for.
l) Central Park (unless there's somewhere else time could be better spent?)
Do you like massive parks? It's sort of interesting just to see how active and bustling the place is though. Also, if you're going to the Met, it's not a bad idea to walk through the park before or after since the Met is actually on park grounds.
m) catch a top show?
Sure, what's a top show to you?
n) any other recommendations on the most impressive things to see/experience if you only have 3 days?
Walking around West Village and Meatpacking District and then taking a walk on the High Line (elevated park) along with seeing the art galleries and the Whitney Museum in the area is one possibility.