TMZ Sports spotted Hampton taking his family to dinner at Catch NYC -- one of the hottest restaurants in town ... where he told us paid for the entire meal himself! And, this place ain't cheap!

Earlier in the day, Hampton -- one of the top-rated high school stars in the country -- announced he turned down scholarship offers from schools like Kansas and Kentucky to play overseas for the New Zealand Breakers in the Australian National Basketball League.

"It's a big deal," Hampton told us Tuesday night ... "I think it's the best route for me and I'm so excited I did it."

So, why this particular team?

"They got a lot of ex-NBA guys that own the team," Hampton said ... "The coaching staff's really good. The team is actually a really good team. They're all bought in and invested in me getting to the league as quickly as possible."

Hampton says the plan is to spend 5 or 6 months overseas before coming back to the U.S. in March to prepare for the 2020 NBA Draft.

And, get this ... now that Hampton can start negotiating endorsement deals without worrying about losing college eligibility, he told us he's looking at his options for a possible shoe deal.

"I'll probably figure that stuff out in the next couple of weeks."

Hampton says his biggest message that he hopes to send to young players is simple ...

"You need to have your own brand. You need to be yourself. You don't need to let others dictate who you are and how you play. Just take control of your future."

Hampton is expected to make his debut with the New Zealand Breakers in October ... and you can bet your ass there will be A LOT of people watching!