Much as we have a (deserved) reputation as haven for gourmands, gastronomic depravity, and dietary overload, with our all-you-can-eat buffets, outrageous eating challenges (see QoD 7/24/09, with "Updates"), gold-garnished desserts, and four-figure truffle-and-foie-gras concoctions (see QoD 8/27/13), Las Vegas these days is actually also a great place to dine out for anyone with a special dietary requirement, from sugar- and gluten-free, to vegan, kosher, halal, and eco-friendly.
When it comes to low-carbohydrate (or low-glycemic) diets, of course the first priority is to have a good understanding of what that means and whether your dietician is recommending an eating regimen that is low in carbs in absolute terms (as in, only 5-10 percent of your calorific intake should be coming from this food group), or if it's more of a relative thing, where you just need to keep on eye on ratios and not go overboard on those starches.
We are not doctors and are certainly not qualified to venture any deeper into the pros and cons of the Atkins Diet and so on, but we can give a few broad suggestions that we hope will be helpful, along with some recommendations of restaurants that we know specifically offer low-carb menus or specially tailored items.
While buffets are commonly thought of in their capacity as gorge-fests, the flexibility offered by an array of food stations can work well for anyone on a quest to cater to special dietary needs. The average buffet will offer plenty of salads and vegetables, carving stations, and ethnic options that allow you to eat well while avoiding piles of pasta or potatoes. These days most also cater to patrons on a sugar-free diet, with a good selection of dessert options that will satisfy a sweet tooth without plunging you into a state of hyperglycemic shock. (We even have a long-established bakery where all the treats are guaranteed to be sugar, corn syrup, honey, molasses, and sucrose-free: Check out Mrs Williams and her daily array of sugar-free and diabetic delights, to be found at the intersection of Spring Mountain and Decatur, just west of the Strip.)
Obviously, steakhouses and seafood restaurants are to be found in abundance in Sin City these days, while we are home to some world-class Japanese restaurants that can accommodate your diet excellently, if you fancy something a little more exotic (there's a lot more to this cuisine than California rolls and tempura!).
For some specific suggestions, P.F. Chang's has several locations around town and is great not only at catering to special diets, but also for listing all their menu items online, with a breakdown of nutritional information. We'd recommend their gluten-free menu if you're looking to avoid carbs and you can check it out on the website before you dine, so you're not sitting at your table for an hour with a calculator, figuring out what might taste good without killing you. Grand Lux Cafe at Venetian is definitely a notch or three above the traditional casino coffee shop, and has always been great on accommodating patrons' dietary needs -- just inform your server of your requirements if you're unsure what to order, and we're confident they'll find an array of options that accommodate your needs. The same goes for Mon Ami Gabi, the popular French bistro at Paris, which offers Strip-side dining with views of the Bellagio Fountains and great people-watching, in addition to menu items designed with dietary requirements in mind. Again, ask your server for recommendations if you're not sure what to pick.