Kanye West & Julia Fox Do NYC, After Miami Double Date with N.O.R.E. -

LATE BITE

Kanye West is in the midst of a pretty romantic tour with Julia Fox, hitting up NYC Tuesday night ... on the heels of introducing her to his close pals, including N.O.R.E., during a whirlwind weekend in Miami.

Tuesday night Ye and the actress did a classic New York date -- a Broadway play, followed by dinner at Carbone. The couple drew plenty of attention as they entered the restaurant.

By the way, they'd just taken in a popular, provocative and perhaps appropriate play -- Julia and Ye had tickets to see "Slave Play." The acclaimed production deals with race, sex, gender, traumatic experiences and ... interracial relationships. It's been nominated for 12 Tony Awards.

The couple clearly loves the menu at Carbone, because that's also where they dined Monday night ... but that was down in Miami, where they had a double date with Drink Champs host Noreaga and his wife, Neri.

For those keeping track, we're told that was date #3 for Ye and Julia, who seemed pretty comfortable as she whispered in his ear during the MIA dinner.

N.O.R.E. and Ye have been friends for years, and here's a fun fact ... Kanye's nickname for his firstborn -- Nori -- is inspired by his old buddy.

Anyway, we're told there was nothing low-key about their outing -- plenty of fans in the restaurant spotted the famous couples and snapped shots with them.

Ye and the actress -- best known for "Uncut Gems" -- have been nearly inseparable since date #1 ... which came New Year's Day in Miami.

Our sources say they managed to keep date #2, presumably on Sunday, more out of the public eye ... but also met up with some of his friends for that one.

We're told the friend that time was none other than Future! No word if he was third-wheeling or had his own date.

In any case, Ye and Ms. Fox are in travel mode now, and with a total of 4 dates, and at least one flight, under their belts ... things seem to be moving quickly.