Early in the film, the Narrator (Ed Norton) goes to a large church to attend a support meeting of cancer victims (where he first talks to 'Marla', played by Helena Bonham Carter). The church is actually St. Brendan's Catholic Church, located at 310 S. Van Ness Ave., in the Hancock Park area of Los Angeles.

This same church was also seen near the end the original (1953) film version of "War of the Worlds", and in a 2004 episode of "CSI" (titled "From the Grave"), where Horatio goes to confession at the church.

In one scene, Ed Norton watches as 'Marla' goes into a coin-op laundromat and steals a load of laundry. That laundromat scene was actually filmed on Melrose Avenue, at a real laundromat named "Laundryland", located at 4371 Melrose Ave., in Los Angeles. (This in the unfashionable section of Melrose, miles to the east of the trendy shopping district, and just east of the Hollywood Freeway.)  *

Helena Bonham Carter then goes to a Vintage Clothes store nearby and sells the items she stole from the washing machines. Afterward, she and Ed Norton exchange phone numbers outside the store. That "vintage clothes" storefront (it's now a florist shop) is nearby on Melrose, just a block to the east of the Laundromat, at 4314 Melrose Ave.  *

Ed Norton comes home to find fire department trucks outside his condo, and learns that his apartment atop 'Pearson Towers' has exploded and burned. The actual apartment building used in that scene was the Promenade Towers, located at 123 S. Figueroa Street (between 1st & 2nd Streets), in downtown Los Angeles.

"Lou's Tavern", the tacky neon bar where Tyler Durden (Brad Pitt) stages the fights and creates the rules of "Fight Club", was an actual bar, located at the northeast corner of Figueroa Street & Harry Bridges Blvd., in Wilmington, California (not Wilmington, Delaware), across from the docks of the port of Los Angeles harbor.

When that nude bar finally closed its doors for good, the makers of "Fight Club" rented the empty building, put up their own neon signs (The "topless" sign in the back was part of the original bar), and shot the key fight scenes there. Not long after filming ended, the entire building was razed to the ground. The address is now nothing more than a vacant patch of bare land (although you can still see the oil refinery in the background...) *

Likewise, the "Paper Street" house, the Victorian home where Brad Pitt and Ed Norton lived and trained the Fight Club members, was also in Wilmington, CA, not far from Lou's Tavern, at 240 N. Neptune Ave. (the southeast corner of Neptune Avenue & C Street).

The production company built the house from scratch on what was then an empty weed lot in Wilmington. (When they first built it, it looked like a brand new house. A few days later, they had "aged" it into the sad state you see in the movie.) After they shot the scenes, they tore the house down and left the lot as empty as it had been when they first found it. Since then, though, the entire block (and several other blocks in the area) have been razed to the ground, to make way for eventual expansion of the nearby Port of Los Angeles. So unfortunately, there is now nothing left to see of either the house or the tavern.  *

There was one other "Fight Club" location in Wilmington. Remember the scene in front of the tire yard, where (as part of a 'homework assignment' to start a fight - and lose) a Fight Club member squirts passersby with a hose? That scene was shot at the Llantera Tire Center, at 505 N. Avalon Blvd. (at E Street), in Wilmington, CA. *

In a similar "homework assignment", another Fight Club member tries to pick a fight in the middle of a public art piece, comprised of large geometric shapes of burnished steel. This work of art, by Michael Heizer, is titled “North, East, South, West”, and it is located just outside the doors of the 48-story office building at 444 S. Flower (at 5th & Flower) in downtown Los Angeles. (It's between the Bonaventure Hotel and the U.S. Bank Tower.)

The also in those "homework assignment" scenes, we see, a guy picking a fight at a Cadillac auto dealership.
This scene was shot on the S. Sycamore Avenue side of Lou Ehlers Cadillac, which used to be at 5151 Wilshire Blvd., about a mile east of the La Brea Tar Pits, in Los Angeles. The 1955 building was torn down in 2008. You can see an old photo of how it looked here.