Logan's Run
Book 2116
Movie 2274
Logan 5 (age 26), Francis 7 (too lazy to research age but assuming same as logan)
movie math: If using Francis, 6 gens back(30*6) + #7(26) may place city starting around 2068 given 30y cycles.
book math: would place city beginning at 1910
Star Trek
Post-atomic horror 2054-2079
First contact 2064
I know it doesnt fit but I always looked at Logan's Run as being in the Star Trek universe given the purge needed to flush out deep rooted culture aspects. It could fit into the after WW3 and before Cochran. Freed young ppl with advanced science/tech, it has made the best sense to me as to how humans over came today's problems to achieve utopian world. Also fits the horror Q talked about from past human history.
Think it could be shoe-horned into ST.