1:34:53: After the crash, Max learns that Vincent is going to kill Annie, the lawyer he met at the start
of the movie.  Finding a gun in the wreckage, and escaping the police, he starts running
to Annie's place of work (the U.S. Attorney's Office), hoping to save her.

The screenshot above shows Max running north up S. Flower Street,
passing W. 6th Street, in downtown L.A., near the Standard Hotel.

The camera is looking south down Flower.

Here is a matching Google StreetView.

1:34:57: Running north up Flower Street after the taxi crash, Max spots a man holding
a cell phone, standing in front of a hotel.  Max steals his phone (and pulls
a gun on him when he objects), before continuing his run up Flower.

That robbery scene was shot in front of The Standard hotel, a popular spot with celebrities.

The Standard is located at 550 S. Flower, in downtown L.A. -
at the northeast corner of W. 6th Street & Flower.

In the screencap above, the camera is looking southwest down Flower,
towards 6th Street, from under the awning in front of The Standard.

(It's the same hotel they used earlier for the downtown skyline
view from that "Fountain Ave" apartment scene.)

Here is a matching  Google StreetView of the hotel.

1:35:37: Max, trying to warn Annie that Vincent is coming to kill her, spots a
sign and runs into the entrance of a parking garage.

Max is still on Flower Street here, as he turns right (east) and runs into the entrance to the
underground parking garage of the Los Angeles Central Library. The Library's official
address is 630 W. 5th Street, and it's at the southeast corner of 5th Street & Flower.

But this entrance to its garage is on Flower, at approximately
544 S. Flower Street (just south of 5th Street), in downtown L.A.

(Note the letter "P", for parking, on the sign above him.)

Here is a Google StreetView of that Library garage entrance.

1:35:40: However, Max doesn't really wind up in the Library parking garage.

The movie switches locations again, as soon as Max is inside the parking garage.

Max  tries to phone Annie inside the garage, but he can't get a cell phone signal, so he runs
out onto the roof of the parking structure, where he finally reaches her on the phone.

As you can read in the screencap above, this scene was shot inside
(and on top of) the parking garage for the 777 Tower,

But while the 777 tower itself is located at 777 S. Figueroa Street, its multistory
parking garage is located a block to the west, at 945 W. 8th Street, in downtown L.A.
(at 8th Street & the Harbor (110) Freeway).

If you've ever spotted that downtown mural of the violinist in a tuxedo,
as you drove the Harbor Freeway - that mural is on this parking structure.

Here is a Google StreetView of the exterior that garage,
with the 777 Tower seen behind it.

In the screencap above, of Max on the garage roof, the camera is looking southeast.

The three skyscrapers seen behind him are, from left to right:
The 777 Tower, The 801 Tower and the 888 International Tower - all on Figueroa Street.

(The director says that the Secret Service parks their cars on the roof of this garage, and
won't let anyone near the roof - making it difficult for him to get permission to shoot there.)

But take note of the shot on the roof (above) where Max looks up at Annie's skyscraper.

That is not the 777 Tower or the Gas Company tower. We'll tell you later where it is.

1:36:11: Vincent goes to the U.S. Attorney's Office to kill Annie.

We see him enter the lobby, get into an elevator, and take it to the 14th floor,
where he kicks down the door to her office, only to find it empty.
Annie is two floors above, in the file room on the 16th floor.

Vincent realizes this and kills the power to the building, so she can't phone the police
for help.  As he stalks her in the darkness, Max arrives and breaks into the lobby.
He confronts Vincent and shoots him, allowing Max to flee with Annie.

Now this should have been shot at the downtown courthouse (at 312 Spring Street),
which is where it's supposed to take place in the movie.

But in reality, these lobby & hallway scenes were actually shot inside the
Gas Company Building at 555 W. 5th Street, in downtown L.A.
(according to Chris W., who works in the building.)

To be more specific, it was shot in the building's north lobby, which doesn't open to the street,
but rather to a patio between the Gas Company Tower and the AT&T building next door,
to the north.  This section is convenient for filming, because it can be easily isolated.

Here is a photo of that Gas Company lobby:
(courtesy of  shootingarchitecture.com)

Note the mural on the wall outside.  It's titled Dusk, by Frank Stella.
Here is a Google StreetView of that mural and the north lobby.

Part of that mural can briefly be seen behind Max when he shoots out the front door:

Here is a Google StreetView of the exterior of the Gas Company tower.

However, the interior scenes of Annie's office - and its window view of the
downtown skyline - were not shot in the Gas Company building.

Take a look at the view from that tower, from Annie's office window:

In the screencap above, see that blue & red building out the window in Annie's office? 
That is the Staples Center. You can also see the Harbor Freeway, to the right.

You don't get that view of the Staples Center from the Gas Company tower.

Remember that earlier shot of Max looking up at Annie's skyscraper?

Those indoor office/window scenes were, in fact, shot from that skyscraper, which is
located at 1055 W. 7th Street (formerly called the ARCO tower)  in downtown L.A.,
about a mile west of the Gas Company tower.

This 33-story building is just west of the Harbor (110) Freeway.

The exterior of the tower also matches up with the earlier view of Annie's
building where Max is looking up at her from the roof of the parking garage,
and the view from the window matches up as well.

Here is a Google StreetView of her 1055 tower.

Here is a map showing all of these downtown locations: