I've been to Mexico several times and absolutely adored it. I took four years of Spanish in high school and enjoy the language, so the culture fascinates me. In visiting Mexico, one quickly learns that authentic Mexican food is not necessarily what one sees in foreign restaurants. It's not just tacos and burritos.
At a not-in-Mexico Mexican themed restaurant, often the very first thing they try to bring you are salty nachos. They're trying to get you to order as many drinks as possible, preferably alcoholic ones :). Send them right back. Get that temptation out of the way.
The main dishes to avoid are the beans and the flour / corn tortillas. In restaurants outside of Mexico, restaurants often use beans as a "cheap filler" to save them money. However, in Mexico, many restaurant dishes are done with fresh seafood and fresh poultry. They don't tend to have dishes which are 90% beans and 10% tortilla.
Look through the menu to see what dishes are available that are based on meat. Instead, order dishes that are straight meat, like beef dishes or chicken dishes. We also enjoy the delicious taco salads that many Mexican restaurants offer. These tend to have flavored beef on top of a delicious salad along with cheese and sour cream.
If you're stuck with the "non-Mexican starchy options", fajitas are great in the sense that they come to you unassembled and you can just eat the delicious innards without bothering to wrap it in the provided pancake. Burritos can actually be handled in the same manner - slice down the middle, open it up and treat the wrap as a 'packaging' that you now eat your meal from within.
In general, a lot of this comes down to if the restaurant actually provides healthy Mexican options or if they only provide "pseudo-Mexican style bean, rice, and wheat" dishes. If it's the second style, it might be time to ask them to add at least one more authentic item to their menu!
Eating Out on a Low Carb diet
Lisa Shea's Library of Low Carb Books
