Hmm. I think that it's hard to find games that really stand up on their own, and haven't had been outclassed in the intervening 35 years. I can think of a lot of games that I enjoyed then, but that's when they were competing against 1980s games and technology. Honestly, you got some of the ones that I'd have suggested, like Tetris and Pac-Man, and even there...I mean, original Tetris is perfectly playable, but I'd probably recommend Tetris Effect: Connected to a new player. Might as well have the extra glitz.
considers
Shmups have generally gotten more fast-moving and bullet-hell oriented. If you prefer slower shmups, you might enjoy playing 1942 or 1943: The Battle of Midway.
I agree with @emb@lemmy.world that Super Mario Brothers 3 for the NES is pretty decent, though I've never played fully through the game. Side-view platformers really did have their heyday in the 1980s and early 1990s, and that was a strong game.
kagis
These guys show marketshare of video game genres by year; platformers were really big in the 1980s:
https://savvystatistics.com/video-game-genres-by-year-1980-2016/
The arcade Teenage Mutant Ninja Turtles (1989) is probably fun if you can get some friends together. Probably need to emulate it with MAME or similar. I don't think that the beat-em-up genre has changed all that much or seen many entrants since.
https://www.youtube.com/watch?v=2jLO1upcd8w
The Simpsons would be a stronger arcade beat-em-up recommend, but that's 1991, a bit out of your timeframe.
https://www.youtube.com/watch?v=WNpuIHbK3-I
Arcades really peaked in the 1980s, before home console systems and computers started cutting into them. There were some things that arcade games were better at than computers and consoles, like having custom-to-a-game input hardware. If you are willing to get ahold of some arcade-style hardware, like an arcade-style joystick (US-style Happ, or Japanese-style Sanwa), you could play some games that were designed around having a full-size arcade joystick.
There are trackball and spinner games as well.
I think that light gun games are out, unless you're willing to obtain a CRT. Maybe someone's made something that can deal with LCD/LED displays.
kagis
Apparently so: https://sindenlightgun.com/
There were a number from the 1980s: