National City, in the TV show, is located somewhere on the west coast of the United States. Most likely, it's located in southern California, just south of the Sierra Nevada mountains.
As you mentioned, there are only a couple of things we know for sure about National City. Three of those things can help us locate it:
- It is on the coast: it has a harbor big enough for a large oil tanker to dock there (the one Kara splits in half by accident). This almost certainly means it's one one of the coasts, as I don't think any inland rivers are big enough.
- It's near enough to some very arid regions that Alex can get there for work and back.
- It's roughly a "two hour drive" from National City to Montecito. From episode S01E06, "Red Faced":
Cat's Mom: Anyway, Toni's having an impromptu little dinner party at the house she's rented in Montecito. Just a few old friends.
Cat: Mother, that is at least two hours away, we're going to have to leave right now.
Fortunately, This last one really helps pin down a lot. Since Montecito is in Southern California, we know National City has to be in the same area. A ballpark estimate would put it within a 120 mile radius of Montecito. If we further restrict ourselves to the coastline, that puts it on the coast, somewhere north of San Diego but south of Los Angeles.
The bottom end of Death Valley would be almost due north of that point on the coast. And being on the coast likely means lots of bays or barrier islands where that bridge would be needed. So, all of the pieces seem to fit a city located somewhere on the southern CA coast between LA and San Diego.