I haven’t watched a Doctor Who episode in a few months and have been feeling the effects. It sounds silly, but after the main seasons got taken off of HBO Max, I started working on a presentation for my friends to explain the whole show. While it’s unfinished, I can at least make a mini version with episodes from 2005-present that you could watch without understanding anything of the lore!
TLDR for those who have no idea what I’m talking about: Doctor Who is a science fiction kids’ show that’s been running for 60 years. With two reboots and several spin-offs. The main series follows the Doctor, a time-traveling alien, as they go on adventures across space.
It is also one of my comfort shows whenever I am having a moment.
Some of these episodes are sadly not available on streaming at the moment. But when they are, and you’re looking for a specific episode to try out, here you go:

The Story and the Engine (Season 2, episode 5)
The 15th Doctor and Belinda Chandra come across a barber shop in Lagos with a thirst for stories, a few hostages in need of a haircut, and a television of memories.

73 Yards (Season 1, episode 5)
Ruby Sunday has been left behind by the 15th Doctor and is now being followed. But when people offer to help her figure out what might be behind her, things take an odd turn.

Blink (series 3, episode 10)
A photographer comes across a hidden message within an abandoned house where the lawn is covered in angel statues. Not weird at all if you don’t blink.

The Waters of Mars (David Tennent special)
The 10th Doctor is traveling alone. Which he never should do. Or else he’ll try to mess with fate. The crew of Bowie Base One, the first colony stationed on Mars, is about to deal with a disaster historically documented.

Midnight (series 4, episode 10)
While taking a scenic tour of a planet made of diamonds, the 10th Doctor finds himself stuck in a train with agitated passengers, and an unknown entity is knocking outside the window.

Vincent and the Doctor (series 5, episode 10)
When the 11th Doctor and Amy go to a museum and notice a creature in one of Vincent Van Gogh’s paintings, they decide to travel back to when he first painted it to find out what the creature may be.

The Power of Three (series 7, episode 4)
Random small black cubes are showing up across the world, and they’re doing nothing. Which is strange. So strange that the 11th Doctor is forced to sit still and observe them with Amy and Rory.
Technically, you could start with any episode and be caught up fairly quickly. Because of characters getting replaced, time constraints, and filming. The Doctor has been played by about 15 different actors (including David Tennant twice). So with that in mind, any first episode of a season with a new person playing the Doctor is great to start because things get explained again as they go. But because I’ve been watching since I was a kid, I just like picking episodes at random to rewatch.