Learn English – the word to describe trying to find the right word for something

If you're committed to a single word, I would look at the reflexive verbs lull, quiet, or ease. Soothe would work.

The resulting sentence would be something like,

"I lull myself by the river."

"She quiets herself by the river."

But, if you want a single unreflexive verb, I would use unwind or relax (somewhat obvious).

"I unwind by the river."

Byronic hero or just Byronic seems close to what you want, but not exactly. A byronic hero is a moody, mysterious, aloof hero, but is also bitter, cynical, defiant, and self-absorbed (here).

Noir hero might do. Frank Miller writes "The noir hero is a knight in blood caked armor. He's dirty and he does his best to deny the fact that he's a hero the whole time" (here). But you needn't stick to Miller's definition. A noir hero is just any hero associated with the noir genre, and the character you describe might fit that bill.