Hello.
Well, December in NYC... since you want to walk around, I suggest you bundle up since it's going to be cold. There hasn't been a significant amount of snow in the city for a while (probably global warming or something), so, if I were you, I wouldn't worry too much about that.
Coffee shops are all over Manhattan, especially Starbucks, but you should probably go to a local one instead there are lots of nice ones in the Village and SoHo and Brooklyn's Park Slope. Do you plan on visiting the other boroughs--you only have 4 days, but both Brooklyn and the Bronx have the Botanical Gardens, the Bronx has the Bronx Zoo, Queens has the Museum of the Moving Image, Staten Island is a wasteland, don't bother lol. There's also the Statue of Liberty which you would have to get a ferry from downtown Manhattan to get to. Manhattan probably has all of the Museums that you want to go to though--the Metropolitan Museum of Art, the Museum of Natural History (these two have "suggested" entrance fees, so just give what you can), and the Museum of Modern Art (which has a $20 entrance fee, unless you're a student and thats $12).
About the Broadway shows--if you want to buy in advance you can look them up online and have them hold the tickets for you until you get there. There's also Tkts which is in the middle of Times Square where they sell tickets for performances that day. There are great discounts, but you'll probably end up wasting at least 1 hour of your day on line--not always, but usually there's a long line. This is their website: http://www.tdf.org/TDF_ServicePage.aspx?id=56
I wrote a lot, but I know I didn't answer all of your questions, if you need anything else, please don't hesitate to contact me again.
P.S. Sorry about Chavez :(. I actually just got back from Ecuador and, for the most part, only heard good things about him there. I'm a political science major at school, so I know that there was definitely a need for a change, but it's a shame that it came at a cost to your democratic rights as citizens. Stay strong!
