What area of Los Angeles does this historical map depict?
That appears to be the survey of LA drawn out by Lieutenant Edward Ord in 1849.
If so, then the Fort Street in the grid-like area in the upper left area of the map later became Broadway street. Hill Street, the next over from Fort Street on the survey, is still the next street NW from Broadway today.
As for where on Broadway that is, I'd say its almost certainly centered around 1'st St. For one thing, LA's grid bends a bit there much like the bend on this map. But more importantly, cities tend to grow outward, with the center of their downtowns typically occupying the area of original settlement.