The thread about telecoms in Canada reminded me of this...
Last time I visited the US (summer 2012) I bought a SIM for my iPhone in a T-Mobile store with a $2-a-day "all you can eat" tariff. It was fantastic for staying connected, especially as my UK provider (O2) charges the equivalent of over $4 for a measly 15MB of data of roaming data, which you "buy" from your current PAYG balance.
(Yes, you read that right. Better than coming home to a roaming data bill for hundreds of pounds, but still price-gouging!)
Is T-Mobile US still offering this (or a similar) service? I tried their website but couldn't find any mention of it, and unfortunately my old US SIM has probably expired by now through lack of use.
ETA: doesn't have to be T-Mobile - my iPhone is unlocked - so it just needs to be available for the 5S (i.e. nano SIM).