I always refer to “The Goldbergs” as “That 80s Show.”
Hogan’s Heroes was set roughly 25 years after the war. The show was on the air longer than U.S. involvement in the war lasted.
The first season of The Waltons aired roughly 40 years after the events depicted, but by the last season it was only 35 years after. One of the reunion movies * A Walton Thanksgiving Reunion* (1993) took place exactly 30 years after the events depicted, which included their reaction to the JFK assassination.
A new Australian comedy, Frayed, which has not been aired yet but is now being promoted is set in 1988. It is about an Australian emigrant to Britain who returns to Australia.
It seems to me that genres such as this appear when the people who would be interested are old enough to have disposable income to throw at advertisers.
Mindhunters on Netflix is a little on the high side of 30 years, but close enough for me. Good series.
NM
The movie Frequency is largely about a time-skipping ham-radio conversation between a father and son, the former in 1969 and the later in 1999.
American Dreams aired from 2002-05, and covered 1963-66.
WildaBeast, there’s a movie called Remember Me that has 9/11 as a plot point. Sort of.
(I was going to mention China Beach, but someone already did.)
This intrigues me. What, if anything, is so special about 1988, and what would he/she bring back to Australia from the experience?
We’re almost as far removed from Summer of Sam (1999) as it was from 1977, when it was set.
Young Sheldon takes place in the '80s. Fresh Off the Boat started in 1989. Maybe they could have some crossover shows with the Goldbergs. 
Deutschland '83 was first broadcast in 2015 (great series by the way, slightly under the radar but worth watching)