One often hears of the official White House chef, or at least (depending upon the president) the availability of pretty much whatever food they might like via delivery at any given time. Have presidents traditionally had unrestricted access to the White House kitchens? If so, have any of them spent a notable amount of time there?
The most famous presidential cooking tradition is the White House barbecue, where the photo op of the president in a white apron spearing hot dogs has been a necessity for more than half a century. Politico has a photo gallery of postwar presidents barbecuing. I'm not sure why they're giving so much "creator's credit" to Johnson, though. Because the president best known for his cooking--the president so devoted to his boyhood Texas style of barbecue that he had a grill installed on a White House porch for his personal use--was actually Dwight Eisenhower. Furthermore, for Eisenhower it wasn't just a case of cowboy American masculinity: cooking--grilling and beyond--was a passion.
He had actually learned to cook as a childhood chore. This turned out to be fortune for a reason that a lot of people today find as a surprise. As America's First Couple in the 1950s, Ike and Mamie Eisenhower worked hard to embody the "separate spheres" idea of suburban masculinity and femininity that, essentially, Betty Friedan sought to dismantle in The Feminine Mystique. Mamie Eisenhower's reputation today remains the well-coiffed, put-together, conservative yet dynamic housewife in chief. But there was a flaw in the stereotype: she couldn't cook. She'd grown up quite wealthy, learning financial management and household administration more than hands-on tasks like cooking or how to use an icebox without flooding the house.
Although Ike initially stepped up and taught her how to cook, they eventually settled into a pattern where that was his domain. While his opportunities to cook as president may have been more limited (though as I said, he spent plenty of time in his private kitchen), he is famous for being host and cook at parties during--of all things--the closing years of World War II in England. His staff from the time even remembers that he insisted on cleaning his own dishes! (Seriously, why, dude.) Eisenhower tried to teach Winston Churchill how to barbecue hot dogs, and was infamous for adding so much chili powder to his barbecue that guests were politely asking where a fire hydrant might be. (Nb: I'm paraphrasing because I don't remember the exact quote off the top of my head--it's something about "all the beer in England" not being enough to damp the heat.)
The Eisenhower Presidential Library's website actually hosts a PDF of his personal recipe cookbook, if you're interested.