I’m very big on watching old-time TV-- Perry Mason, Route 66–but Alfred Hitchcock Presents is in a class by itself. Nostalgic? Maybe. But “comfort TV”? Definitely not. I still have psychological scars from the episode entitled “An Unlocked Window.” 
It ran from 1955-1962, 268 episodes with Hitchcock directing 17 of them. Hitchcock himself appeared at the beginning and end of each episode to introduce it and to wrap up. Here’s an interesting comment from the Trivia section of IMDB.com:
Most people who have seen this series remember Alfred Hitchcock’s opening and closing narratives for the series. However, for each episode, more than one opening and closing was filmed, as Hitchcock’s famous jibes at the sponsors were unappreciated in the European markets. So for each episode, Hitchcock filmed two openings and two closings: one would be for American viewings (jokes about sponsors) and the second would be for European showings (jokes about Americans, and not about sponsors). For most of the third season, Hitchcock even did the opening and closings in French and German, as he spoke both languages fluently.
The series is available on the Roku channel-- not sure how you access it if you don’t have a Roku. Watching TV used to be so simple… not any more.
I just watched the first two episodes of season 1 – no comfort in either one, but Hitchcock grabs your attention immediately.
To quote one of his wrap-ups, “The cold New England sun slowly sinks behind the coroner’s office…”