So I've got a couple of services that I access using mydomain.org:1234 for example, but since Nextcloud runs its own web server it's hosted on mydomain.org/nextcloud.
How do I set up my services so I can access them from a friendly URI like Nextcloud instead of ports?
You want a reverse proxy. But if nextcould is already reserving ports 80/443 you need a bit more configuration as it's not possible for multiple processes to use the same port.