Interested in US/UK stations mostly, but if you know of what was happening elsewhere on TV around the globe during this time, or of any countries that had a TV service at that time but didn't air it (or couldn't), that would also be interesting. What were they showing in the USSR for example?
In the UK, Bing Crosby and Lulu.
There were three channels in 1969: BBC1, BBC2 and ITV. There was coverage during the week of the launch and regular updates, on the evening of July 20th both BBC1 and ITV had extensive moon-based programming including the live landing just after 9pm local time. The BBC had a programme featuring live pictures from the command module at 6.45pm, the landing itself from 8.45pm, and from 10pm So What If It's Just Green Cheese?, "An entertainment for moon-night", featuring Judi Dench, Ian McKellen, Dudley Moore and The Pink Floyd playing a jam called Moonhead, with programming continuing through the night (a rarity, television usually closed down in the early hours of the morning) for Neil Armstrong's first steps. ITV's coverage was hosted by David Frost and featured a variety show with Engelbert Humperdinck, Cliff Richard, Cilla Black, and Lulu, and a rather varied panel including A.J.P. Taylor, the Bishop of Woolwich, the athlete Roger Bannister, and Sammy Davis Jnr. "Between the two channels you can settle for awe or haw-haw as the mood takes you", as the Sunday Mirror put it, continuing "If you want to stay at ground level, try BBC-2. They offer forty-five minutes of Lulu in colour without the word "Moon" being used once. The show was made in Sweden some weeks ago."
BBC2 had featured Apollo 11 coverage earlier in the evening, but if you were inexplicably uninterested in the moon then at 7.25pm you could enjoy From Amazon to Orinoco by Hovercraft; at 8.15pm Musicamera, a contemporary version of the Mussorgsky-Ravel Pictures at an Exhibition for moving pictures and orchestra; 8.45pm was a repeat of The Bing Crosby Special; 9.35pm saw Children Talking: Love and Marriage, a series interviewing children between the ages of four and eleven on a variety of subjects; 9.45pm was Lulu's aforementioned Stockholm show; a play at 10.30pm in Thirty-Minute Theatre; news at 11pm; and Film Night at 11.10pm, the weekly look at cinema.
The BBC's Genome Project has full listings from The Radio Times for the BBC, ITV's details from The Sunday Mirror, July 20th 1969.