You WILL need a credit card, hotels won't take cash for example. I used my VISA card to withdraw cash as I needed it - I used the machines inside the shopping centre at Columbus Circle - we were staying close by. a nice quiet environment with plenty of security. The market in the basement there is pretty good too.
Taxis from the airport are fixed price ($35 last time I was there) to Manhattan addresses BUT the return fare is a "normal" one, and can be quite expensive. As you'll be jet lagged I'd suggest the taxi into Manhattan, but returning to the airport you can get a subway train for the fixed fare of $2 (may have gone up now) to close to the airport (can't remember the stop) then change to the Airport shuttle train, which was $5. Subway maps are readily available, and you can buy multi-trip "travel cards" - was 6 for $10, and these can be topped up at subway stations.
Make sure you see Chinatown - close to Ground Zero so an easy hop. The view from the Empire State is good at sunset - especially that of the Chrysler building. If you buy a ticket and the visibility is low, you can get the ticket stamped as such (obviously without going up - they tell you at the bottom what it's like) and can use it another day when the view is clear.
Don't know where you're staying, but when we were there we stayed in Midtown on W57th st, and found a really nice southern/cajun style restaurant on 9th Ave around W50th. Also a good diner at the junction of 9th and W57th.