Both Nightmare and Dream don't actually really have to eat, considering their nature, but they both enjoy different tastes and textures, even things that aren't supposed to be edible in the first place. The social aspect also plays a part in it, but Dream does so out of genuine enjoyment and wanting to be close with friends, meanwhile Nightmare does it to foster some sort of bonding activity for the workplace aka the most dysfunctional family dinners known to man.
For all his refinery and preference for more elegant things in life, Nightmare vastly prefers homey foods, especially beef bourguignon or other stews. That preference he shares with Dream, who cooks those often mostly for small moments of pleasure and memories of better, softer times.
They both also enjoy alcohol, but in that they branch out in different tastes; Nightmare mostly likes wines, and probably even has a cellar entirely dedicated to collecting and aging different wines. He also turns his nose up at, what he calls, "classless" liquor, which are basically any spirit used to get fucked up at college parties. Meanwhile, when Dream freshly arrived in the Omega Timeline, upon the question of what his favorite drink is, he nervously declared it to be fruit juice. The truth later came out when a medieval-adjacent AU moved into the OT and brought their own mead, which Dream basically downed a whole keg of and still remained coherent. Not only did everyone find out Dream loved most meads, but he's also got the alcohol tolerance of a seasoned frat-bro (do NOT tell Nightmare, he'd be appalled).