The big Kansas City tight end hit Geraci's Slice Shop in downtown Cleveland yesterday, 87's old stomping grounds -- where the owners of the shop just had to take a pic of their native son.

The photo shows TK standing alongside an old-school payphone in the shop. The caption on the store's Instagram hypes up Travis while also begging him to bring T-Swift into the restaurant next time around.

We talked to an eyewitness who confirmed Swift's absence ... telling us Travis came in with a couple buddies -- all dudes -- in the afternoon and ordered some slices to go.

We're told Kelce was smooth and very down to earth while ordering classic pepperoni and a slice called the "Hot Tito" ... red sauce, mozzarella, thick-cut pepperoni, sausage, romano and hot honey drizzle. That's a meal for a champion to be sure!

It seems Kelce's familiar with the local chain ... with our source saying he's hit up another location in town before, but he's never been to this specific spot.

We don't know how much Travis spent -- but, most slices cost $6 ... a pretty reasonable price for a dude who's making $12 mil next season, not including endorsement dollars.

Now to the heart of the issue ... no Taylor Swift in Ohio it seems. The happy couple was recently reported to be enjoying a vacay down in the Bahamas -- so maybe Tay needed to get back to work.

She finished shows in Singapore earlier this month ... and, we know she's not scheduled for another live show until early May in France -- but, she's a busy woman and may have other obligations she needs to get back to.

They've hit a bunch of incredible locations together ... Argentina, Australia, Singapore, Las Vegas -- but, interestingly enough we haven't caught them in Travis' hometown before.

Taylor's a music legend by now ... so, it seems only a matter of time before she hits the "Rock and Roll Capital of the World."