David Harbour Smiling in NYC With Female Friend After Difficult Few Months

David Harbour seems to be taking it easy after a difficult few months ... with a companion putting a grin on his face in New York City earlier this week.

The actor hit the Big Apple Tuesday night ... trying to keep a low profile while walking through Times Square.

Harbour's got a hat and thick jacket on ... keeping his head down and focusing on conversing with the woman at his side, who's bundled up in a long white coat.

It's unclear what the nature of their relationship is -- we've reached out to his team to get to the bottom of it -- but they clearly have a rapport ... and we are told they went to the hit Broadway show "Chess" together. No PDA between them as far as we know, though.

Earlier in the day, Harbour was snapped enjoying a smoke while taking a stroll through the streets of The Big Apple. He was all alone, which has been a common theme for him since his divorce from Lily Allen played out over the last few months. You may recall, Allen was seen smooching another guy -- Jonah Freud -- at a holiday party last month.

As you know ... Lily and David separated early last year -- before she alleged he cheated on her in her album "West End Girl."

On top of his marriage ending, Harbour landed in the headlines after his "Stranger Things" costar Millie Bobby Brown reportedly filed a bullying and harassment complaint against him. Millie talked about how much she enjoyed working with David during the recent press tour for the show ... seemingly shooting down the report.

Plus, we viewed video of Harbour stealing a guy's hat at a bar, spiking it to the ground and then ranting about the Iraq War. Harbour has a documented history of bipolar disorder ... and our sources told us they wouldn't be surprised if the stresses in his life caused an episode.