Venice, 1817. And no, not Venice, California. Venice, Italy—the real Venice, the Venice after which the California one was named, the city that is surrounded by water where everybody uses boats instead of cars (and canals instead of roads). That Venice, folks. This is where Byron was living when he wrote the poem in 1817. Venice was an important place for Byron, and an important place to keep in mind as you read, even though, technically, it's nowhere to be found in the poem itself.
Still, from what he tells us in his letters, Venice in 1817 seemed like a pretty happening place, if you had money and connections that is: dinner parties, nighttime boat trips, balls, and all that good stuff. In the letter in which he included the poem, Byron tells us that the Carnival has just ended. Just before Lent (i.e., the 40-day period leading up to Easter), the Venetians would hold a party in San Marco Square, complete with masks, costumes, and dancing. The combination of the Carnival and staying up really late were too much for Byron, and prompted him, in part, to write the poem.
If this is the background setting to the poem, what about the setting in the poem itself? We might best describe it as "afterwards." Clearly, our speaker is looking back on his past shenanigans, and resolving not to repeat them again. In that way, he's all about a change of scenery, even if it's not literal scenery in the poem. We can guess from Byron's bio that he would be looking back at the wild times in Venice. Still, without those details in the poem, we can more safely say that the poem is set in our speaker's mind, which is in a reflective, but newly determined, mood.