Any tips for how to do this? I try to be a follower of the "show, don't tell" rule, so I feel like I need more than just saying something is a "huge, sprawling metropolis, bustling with activity and peoples of all description". I have a hard time realistically plotting out large areas, because I often find myself creating way too many irrelevant locations, and reusing the same key ones over and over anyway. So... What do?

Break up the city into districts. Describe the districts and the sort of people and locations you'd find there, give a key location or two, but keep the rest vague until otherwise required. Especially if I'm providing a map.

I struggle with this too wrt my setting. I do the districts thing. One thing is that cities aren't really planned all at once even though that's how we're designing them, so it's good to mix them up and make them feel incongruent to give them texture. Place buildings together that don't really make sense. I try to convey the sense of a lot of people squeezed together a lot, because people can then extrapolate that the busyness is similar all over the city. I also try to put more time into describing travel rather than just letting the players arrive at their destination. It 'slows' down travel and it's a good way to insert a lot of the texture that the players otherwise won't interact with, allowing them to see the transition from neighborhood to neighborhood.

I think "show, don't tell" goes out the window when you're DMing in person. Your players have a finite attention span, and they want the goods - so give them the goods. Tell them they're in a giant city, then fill in the details as they poke around.