The creators never specifically mention where the Arnold's live. This was intentional because they wanted the audience to think it could have taken place in any suburban neighborhood in any town. They did not want to single out a specific city, state, or part of the country.
Some clues that it was set on the West Coast:
-The exteriors of the Arnold house was filmed in Burbank, California. Palm trees are visible in many shots, and the cars have California plates.
-In "The Wonder Years: Wayne on Wheels (#3.3)," a close-up of a letter shows the Arnold's address, which is clearly in California. Wayne's thumb is covering some of the details, but the visible portions read:
Wayne J. Arnold
86-- ---den Place
C---- ---ty, Ca. 90230
The ZIP code, 90230, is for Culver City, CA. There is a "Hayden Place" in Culver City, California (with the ZIP code 90230), which seems to fit the blocked out area of the address; however, "Hayden Place" is in a very industrial neighborhood near The Culver Studios and Sony Pictures Studios.
-In an early episode, Paul shouts that Kevin has a Jets jacket but has never even been to a game.
-It never snowed. However, on "The Wonder Years: Stormy Weather (#5.21)," Kevin mentions his dad once being stuck in a blizzard.
-If you look closely on one episode Kevin's license said "State of California."
-If you look closely on other episodes the license plates on the cars look like California plates.
On "The Wonder Years: Pfeiffer's Choice (#5.10)," which aired in December, Kevin and his family are invited to a country club with the Pfeiffers. They are all dressed for warm weather which would likely only happen on the West Coast. The episode likely took place mid-way through the school year (around December) because Kevin mentions Paul leaving prep school after a couple months.
Some clues that it was set on the East Coast:
-Kevin wore a New York Jets jacket and had pictures of Joe Namath in his locker.
-In one episode they mention going to Ocean City (which is in NJ or MD).
-Kevin's dad and Paul have noticable New York accents.
-Kevin's dad says that he is originally from Newark (most notably a city in New Jersey) and Jack's dad seems to live within driving distance of the Arnold's.
-If you do an Internet search for "norcom" (the place where Jack worked) the first site that comes up is a corporation in Connecticut.
-In "The Wonder Years: Back to the Lake (#5.23)," where Kevin and Paul return to the lake so Kevin can see Cara again, they drive north on a state route 17, and on the return trip Paul is heard describing a route back home that involves getting back to I-91: both highways are near each other in Connecticut, though I-91 continues through Massachusetts and across Vermont.
-In "The Wonder Years: Summer (#6.21)," Kevin's friends, Chuck and Jeff, mention going on a cross-country road trip. They mention going to New York, New Orleans, and then San Francisco. The fact that they mention New York first and San Francisco last implies that New York is closer because why would you take a road trip and start with the further destination.
-In the second episode, http://www.imdb.com/title/tt0750367/, footage of Arlington National Cemetery is shown. The Coopers also have people back to their house after the funeral which puts them in a suburb of DC.
Cities that can be eliminated as settings
-On the episode "The Wonder Years: On the Spot (#3.5)," Kevin mentions that Winnie's dad flew in from Chicago to watch the play. Unless Mr. Cooper has his own jet, this would eliminate Illinois as the setting.
-On the episode "The Wonder Years: The Ties That Bind (#4.7)," Kevin's mom mentions that his dad will miss Thanksgiving because he has to fly to Pittsburgh and later Denver. This would eliminate those cities as settings.
-In the episode where Kevin's mom works at his school, the baseball game being televised while the family is sitting in the kitchen is Pittsburgh vs. Philadelphia. Since the episode takes place during the week, one of the teams must be "local" as per the time period.