Taylor Swift is getting to know Travis Kelce's old stomping grounds ... because it looks like he's showing her around his home state ... Ohio.

The couple was joined by a third wheel ... and the sighting comes after Travis played in a charity golf tournament Monday in nearby Chardon.

Travis is from Northeast Ohio -- Cleveland Heights to be exact -- and it looks like Taylor is learning more about his roots.

Taylor and Travis were in New York City over the weekend for a fancy dinner ... and now they've traded the Big Apple for the Buckeye State.

Locals were quick to pick up on the sighting -- Taylor's the most famous singer on the planet after all -- and folks are reportedly flocking to the restaurant to try and catch a peek ... but it's likely Taylor and Travis are long gone.