NYC is a great place to bike and a horrible place to be in a car. There are only a handful of circumstances where a cab can beat a bike time-wise. Depending on where you are spending your time and how many people you are with (and their ages) a 7-day Citi-bike membership could make sense.
(It is a shame the tourist passes are so expensive relative to the annual as the annual pass is the best deal in NYC. My annual pass ($95 in year one and now 6 months into $95 for year two) has saved me at least $1,200 in the past 18 months on subway fare, personal bike maintenance, and gym membership.)
I'd also add that most tourists seem to have to see all these things that are like an hour+ apart ("Let's go to the Statue of Liberty, Times Square and the Natural History Museum! they are only like 4 miles apart each!"), but Manhattan has a habit of repeating itself every couple miles so don't force going too far. Try to spend your time in the neighborhoods (pick one or two of Chelsea, West Village, East Village, Upper West Side, lower east side) and if you really like museums, I'd recommend go to the smaller ones like the Tenement or Transit museum.
Walk on the Streets and not just the Avenues. Don't try to see everything. Don't get annoyed when people bump into you and don't say sorry.
