How do I delete a host or metric from the UI?

Metrics

There is not a way to immediately delete a metric, though they'll age out of the UI naturally over time.

Hosts

If you're running the agent, assuming you've intentionally stopped or removed your host, all hosts or metrics that have not seen data in 24 hours will disappear from the UI, you may still query against them though it will not appear in drop downs or the infrastructure or host map views.