My key piece of advice when planning for your trip to New York is to do you research. I know, a headache but it will serve you well when you are on the ground.
I would suggest making a list of everything you would like to do and then map the ideas out by neighbourhood per day in a written schedule. I would pay attention to open and closing times of establishments. Make reservations where you can. Some establishments won’t take reservations as a side note.
I also like to follow social media sites for musuems, galleries, restaurants etc.. Sometimes you can get deals or special promotions if you keep an eye out in advance. Additionally set mobile alerts to these accounts. I liked the MTA.info and TimeOut NY mobile alerts.
In terms of sports tickets, if you are travelling from overseas you may want to buy your tickets in advance. I lucked out and grabbed $12 USD Yankees tickets against the Blue Jays on the same day when I used my Mastercard. I simply walked up to the window at Yankee Stadium and scored the deal. Now a bit of a risk but my pocket book thanked me.
In terms of planning out your day’s using the New York Subway, my suggestion would be to grab a subway map and pick a neighbourhood location that you are planning on visiting that day. Then walk around that neighbourhood and visit alternate points of interest. Take your time and visit local coffee and food establishments. Then get back on the train (or walk!) and visit the next closest neighbourhood in your itinerary. This way you can get to know neighbourhoods, their local arts and cultural spots and eateries. You can cover more ground and have a more through understanding of neighbourhoods. If you are in NYC for seven days grab a MetroCard with a 7 day unlimited window. After the 7 days has passed and if you are staying longer in NYC, top it up a few dollars everyday as necessary.