Laury Palmer may be dead, but her next-door neighbor Mrs. Kraft will never forget her. She is determined the rat who killed her will be found and in the scenes that follow hires a detective to make sure it happens.
Then ... Back in Reno we are introduced to the detective Matthew Arnett (Walter Slezak) while he has his morning cup of coffee. The coffee shop scene was filmed on a sound stage but we can infer its location by the kitty-corner window view showing a glimpse of the Reno Arch.
... in the 1940s ... in this contemporaneous image from a vintage postcard the building at far left is the corner building above. Part of Harolds Club, it was on the southeast corner of Virginia Street and Commercial Row (map).
... in 1955 ... the same block was seen behind Kim Novak in the Reno heist movie '5 Against The House'. Again we can see a glimpse of the Reno arch slogan. By then the corner building had been changed - compared to the Then image above it has many more windows on the second floor.
... and Now, that whole block of casinos has been completely rebuilt since arch-rival Harrahs took over Harolds. In 1963 the arch was replaced by a redesigned version (the old one can still be seen five blocks away at Lake Street by the bridge over the Truckee River). That in turn gave way in 1986 to yet another arch, still there, below.
So the virtual location of the coffee shop was kitty-corner from the above on the northwest corner of Virginia and Commercial Row. Instead of a coffee shop there was a Flying 'A' gas station at that location back then.
... and Now, the county courthouse has not changed.
Despite being taken aback at Arnett's nerve in asking for a $500 advance she hires him anyway. (The wiley gumshoe had already found out that Mrs. Kraft had inherited Laury's house and money).