The '60s have been a wellspring of creative inspiration lately, from Mad Men to X-Men: First Class to Motown-inspired singing sensations such as Adele, Duffy and Amy Winehouse. In the article "1962" in Intelligent Life from the magazine the Economist, author Matthew Engel discusses other recent works of fiction that are firmly grounded in the '60s, including The Help and On Chesil Beach.
Although he doesn't mention King's 11/22/63 in the article, he does write about the strange juxtaposition between schoolchildren of that era experiencing nightmare-inducing take-cover drills at the same time as a "very American sense of invulnerablilty." Other contemporary influences he cites are Rachel Carson's book "Silent Spring [...] inspir[ing] the environmental movement. Nor did anyone spot the future impact of Anthony Burgess's nihilist novella A Clockwork Orange [...]. The author came to hate it too, but the film, made and then withdrawn by Stanley Kubrick, gave it a lasting resonance."
Engel goes on to write, "The where-were-you-when moment of that era — the equivalent of 9/11 in this century — did not come for another year [after the Cuban missile crisis], when JFK was assassinated." I remember a teacher of mine voicing a similar sentiment when I was growing up. That is, that decades later, he could still remember clearly where he was and what he was doing when he first heard about the JFK assassination.
In interviews, King mentions that the time-travel plot is influenced by Time and Again by Jack Finney, who he also acknowledges in the afterword of 11/22/63 and who he mentions would have received the book's dedication, save for the arrival of his granddaughter Zelda. I found a pretty thorough list of time travel science fiction in Wikipedia, many of which can be found at NYPL. I can vouch for Ken Grimwood's Replay being good. Originally published in the '80s, it was re-released in a new edition a few years ago. At one time, there were even talks to film a movie with Ben Affleck in the starring role.