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I'm currently in Mexico (Quintana Roo state) and need to enter the U.S. through a land border crossing. My plan is to fly to an airport near the border, take a cab to the crossing, and then walk into the U.S.

From Cancun airport there are direct flights to Reynosa, Ciudad Juarez, and Tijuana. The U.S. State Department says "Do Not Travel" to Tamaulipas state, where Reynosa is located. Tijuana and Ciudad Juarez seem to have some of the highest murder rates in the world.

Would it be safe to go through any of these three? I'd take a cab from the airport directly to the crossing.

EDIT I have lost my passport, so it seems that the CBX bridge from Tijuana airport is unfortunately not an option.

EDIT 2 I'm not a U.S. citizen but have a green card as well as a U.S. drivers license, which I'm both carrying with me.

For $30, you can walk directly from the Tijuana baggage claim to the United States border via CBX (Cross Border Xpress). That seems like the safest option, even if the others are not very dangerous.

It does require a passport, however, so if your need to use the land border is motivated by a lack of a passport, it looks like this won't help you. Their Requirements page notes that

It is mandatory to have your official travel documents to access the bridge and these may be requested by CBX staff.

In a comment, you said:

Yes, I lost my passport, so the CBX bridge is unfortunately not an option. Should have mentioned this in the question (will update).

As you do not have your passport you might consider going to the US consulate in Cancun to get a new one. They can get you an emergency passport in a matter of hours if need be. Given Cancun's tourist industry, I can only imagine that this happens frequently and they can deal with it quite efficiently.

In an edit, you said

I'm not a U.S. citizen but have a green card as well as a U.S. drivers license, which I'm both carrying with me.

Why didn't you say so in the first place? You should h able to fly directly to the US with your green card. Permanent residents do not need a passport to enter the US. You should also be able to use CBX with only the green card. The fact that the website doesn't mention this seems more likely to be a fault of the website than anything else, since it leaves several cases uncovered, including that of green card holders.

I live in Tijuana, and cross the border at the two Tijuana ports of entry regularly without issue. If you stay away from the dodgy parts of the city (eg the red light district) and don't do anything stupid you'll be fine and safe.

People cross in the US without a passport regularly here - you'll be asked more questions and need to prove you're a US citizen (a birth certificate or driver license is usually enough).