S.I. Swimsuit Model Hannah Davis -- Hangs with Unemployed Baseball Player

Hannah Davis has a heart of gold -- she gave some out-of-work guy the time of day and a cup of joe today in NYC.

The S.I. swimsuit hottie walked out of a coffee shop in the West Village with the guy ... who was dressed in ratty jeans and a t-shirt. She even allowed the idle dude to chat her up for a while.

Clearly, he has nothing to do with his time.

Hannah was also flaunting a ring on her left hand. It doesn't appear to be an engagement ring, but she probably just wants the guy to think she's taken.