You're limiting to '77-'83?!? The quintessential, or my quintessential? Classical only or of all time? Arcade game or arcade hall? Most number of good games released, or most good games out in arcades, or highest good/bad game ratio? Highest number of people, or best types of people, or before it got too crowded?
I ask because for me, there are three very distinct periods for arcade games, classic ('80-'85), my teen years ('86-'91), and post high school ('92-on). My quintessential years were during my teen years, and of those I'd pick '87 or '89. Not only did I get to go out on my own to the arcades, but most of my favorite games came out during those years, and all my classic favs were still out in the arcades. As far as games go, '89 was the biggest year in number of favs released for me, plus the '87 games were still in the arcades. However, the arcade I went closed somewhere around '89-'90, and its decline started a year or so before that, so '87 was a better arcade climate for that arcade. (The pizza joints arcades, 7-11, and the other arcade were still humming in '89 though.)
I can't say the classic years were my quintessential, mostly since I rarely got to play, and mostly at a small pizza joint not arcades, and as I said above those great games were able to stick around to my teen years anyway. Still '82 & '83 released quite a few (just over half as many of my favs per year) as during my teen years. '84 had quite a few good games, too, but it also marked the release of the nintendo VS cabs; they were not arcade quality of the time and took away space from real arcade games. By '86, most of them were gone from the arcades I went to, just in time for my teen years.
Side note: before doing research, my first guess was that '85 was my year. However most of the games I (mis)remembered playing that year weren't released until 2-5 years later.