This poem is set in a sad and lonely city on a sad and lonely night. In fact, even the streets are sad. Oh yeah, it's also raining.
This could be any city in New England, where Frost spent most of his life, or it could be London, where he also lived for a little while. If the poem is indeed in London, then the clock in the sky could be an actual clock – Big Ben – and not the moon. This would still be a pretty lonely and creepy sight. Think of a film noir movie, with shadows everywhere and dangerous characters lurking in the dark – and then tone it down to imagine a normal city, with normal mud and trash: the shadows are only in our imaginations. This is the kind of night we think the speaker is describing – a normal night turned sad and spooky by his inner ambivalence and depression.
Now, we're not sure, but we think that this poem takes place on multiple repeated nights in this city, or many cities, because "I have been" is repeated, and could be setting up multiple scenes. Either way, the scene is dreary and ominous. People are crying out somewhere far away, and the watchman isn't very friendly.
This doesn't seem like a very safe or comforting place to be walking around alone at night – we sure wouldn't want to do it (especially if it was rainy). But at the same time that it's creepy, there's a strange beauty to the darkness and the moon (or Big Ben). In a city like this, on a night like this, we'd want to stop for a moment and look up to the sky. But we'd be sure not to linger too long; the watchman, or worse, could be around the corner, past the farthest light.