I've been asked if it's okay to set the diner stories in different time periods. Diners themselves go back to the late 19th century, when they started as portable lunch carts. Their boom time was really in the years from the Jazz age to the 1950's. As fast food franchises popped up from the late 50's and on, diners were fighting a slow battle for existence.
These days, diners are almost a dying breed. A lot of mom and pop shops are going strong out of pure force of personality. It's also up to the people to keep these places alive. Your story should bring such a place to life no matter when or where it is set.
If you're going to set your diner in a particular era, I suggest you do your research. I don't expect a thesis, but believability is key.
Now suppose you're writing a fantasy about a diner in ancient Egypt. Fair enough. I did say no restriction on genre. So make me believe it. Or at least, make me suspend my disbelief. I can't tell you how much I'm looking forward to reading submissions.
Good writing . . . and good dinering.