It was back in August 2009 that we last tackled this QoD, and a couple of things seem to have changed in the interim. As is common outside of Las Vegas, many of the poker rooms here will offer tableside dining, so you don't have to leave the game. For example, players in the Wynn poker room may order from Zoozacrackers deli, Allegro, Red 8, the coffee shop, or room service (the latter two options are available 24/7, and Allegro is open until 5 or 6 a.m. daily). Caesars Palace will deliver food to poker players from Munch Bar, and the Stratosphere delivers from Roxy's Diner's menu, while Red Rock's poker room used to offer tableside service from both room service or LBS Burger, but now only from the former. Binion's, MGM, Palms, and Venetian are among other poker rooms that will offer players tableside dining service.
When it comes to options for slot and other table-game players, however, the options are far more limited. It was Palace Station that first introduced food service to Pit 8, the Asian gaming pit, back in 2006. We encountered some language barriers this time around, from both the pit staff and Food Express, but as far as we could ascertain, a traditional tableside noodle menu is still available daily from 6:30 p.m. until around 2 a.m. from the popular Chinese eatery on property.
The Riviera has also since introduced this service to its Asian-gaming pit, but only for high-limit players, we were informed when we called (the website seems to indicate that any player can partake of the service, so check with the pit and you might get lucky). The menu comes from Banana Leaf restaurant.
The only other casino we know of that will serve food to players at both table-games and machines is the El Cortez, which introduced this service back in 2007. The special "Gourmet Gambler" menu comes from the coffee shop and is available to all players -- pit and slots -- featuring a selection of items from the coffee shop. Back in 2007 when we first researched this, there was an automatic $1 discount on the regular price for players, but we were unable to verify if that still applies. You can pay with cash, chips, or points and to the best of our knowledge the Gourmet Gambler menu's available daily from 7 a.m.-10 p.m., but we recommend you check with the pit.
If any players can offer any further tips on tableside dining options, we'd love to hear from you and will post an "Update" to this answer.