No problem. The current writer recalls when she was first in Las Vegas back in the late '90s and was filming documentaries, with shoots that often ran on into the night. Our crew encountered the same problem, with nothing but coffee shops and fast food to choose from, as far as we could tell, neither of which was appealing when we wanted to relax at the end of a hard day's work.
However, for one thing there were other options available, we just weren't in the know; for another, the late-night dining scene has come on leaps and bounds over the past decade and, with the sad loss of Ruth's Chris west (an LVA late night staple for carpaccio, escargots, and killer French onion soup) notwithstanding, there are numerous interesting options for late-night munchies.
Some of our favorite options, like Diamond China, Raku, Firefly, and Sake House Ichiza, are off the Strip, so don't fit your criterion, unless you want to take a quick cab ride (easy enough to get there, but you could be in for a long wait getting back). There are plenty of places to choose from in the casinos, however, without having to resort to coffee shops and delis (although if all you really want is a snack, some of these will serve you well. You can use other readers' ratings as a guide to the better options -- see link below).
Wolfgang Puck Bar & Grill (MGM Grand) just added a late-night menu, served from 10 p.m.-6 a.m., for example. SushiSamba at Palazzo also serves a late-night menu from 11 p.m. until 4 a.m. We recommend Noodle Asia at the Venetian, which serves until 3 a.m. nightly.
For something less fancy, Toby Keith's I Love This Bar & Grill (Harrah's) is open until 2 a.m. weekdays and 3 a.m. on the weekend and Stripburger (the al fresco eatery opposite the Wynn in the Fashion Show Mall) serves until 1 a.m. during the week and 2 a.m. on the weekend (perhaps still a little too early for your requirements, but recommended, nonetheless).
Those are just a few suggestions. You can find plenty of other options in our Dining section. Just select "Late Night" from the "Other" drop-down menu and then use the column headers to sort the search results by location, cuisine type, or price.