Helga's Makeover/The Old Building - S1-E4
Trivia: Helga walks by the "Law Office of Garcia, James A."; Tricia Garcia is the storyboard artist for this episode.
Monkeyman! / Buses, Bikes and Subways - S5-E1
Trivia: The banana warehouse at the dock says "ROB RTSON" on top; Chris Robertson is one of the show's artists.
Crabby Author / Rich Kid - S3-E17
Trivia: The book publisher's name is "H. MacDonald"; Hugh MacDonald is a layout designer.
Downtown as Fruits / Eugene's Bike - S1-E1
Trivia: Eugene's bike has a "YOOJ" (pronounced like "Eugene" without the "een") license plate.
Freeze Frame / Phoebe Cheats - S2-E8
Trivia: Arnold's computer is made by Purdy Electronics; Joseph Purdy wrote the episode.
Sid's Revenge / Roller Coaster - S3-E8
Trivia: There are two versions of this episode. Originally, the closing credits appeared over the ending scene with Eugene going around and around in the roller coaster. When Nickelodeon switched to its "squeezed" credits format, a second version was created with the credits removed from that scene, and a new set of credits (over the "normal" credits background) added to the end. (This was later done with "Principal Simmons" as well.)
Benchwarmer / Cool Jerk - S1-E11
Trivia: The water tower at the end says "LOWTWATER"; Steve Lowtwait is a layout designer on the show.
Trivia: All of the cars seen in Hey Arnold! are classic cars. You never see any modern cars - cars made after 1979.
Downtown as Fruits / Eugene's Bike - S1-E1
Trivia: At the beginning, Iggy can be seen very briefly without his sunglasses.
Trivia: Ms. Perfect is the only episode where Arnold does not have a single line.
Love and Cheese / Weighing Harold - S4-E7
Trivia: In 'Weighing Harold', when Arnold is in the comics store, there are comics in the background referencing other Nickelodeon shows, "Catdog" and "Spongebob Squarepants." The former had aired almost exactly a year before this episode did ('Catdog' premiered on 4/4/1998 and this episode on 4/7/1999). The later aired about a month after this episode.
Answer: The show is based in present day times. Plus most cars aren't old fashtioned, I recall seeing a limo and not to mention a cherry picker, etc.