As someone who has thought about this remote style, but hasn’t done it, I don’t think I’d want to be in the hotel room much. I’d much rather find a coffee shop to work from where I can get some of the vibe of the city while still working.
Otherwise, you’d only get a few hours per day in the evening of experiencing anything you couldn’t do at home, so what’d be the point of spending home rent +hotel +travel for the week?
I suppose it depends somewhat on why you're there and how well you can work in an ambient social environment. Mind you, I don't really disagree but, if I'm focused on a computer screen, I'm not sure how schlepping my laptop to a random coffeeshop is that different from being in my hotel room.
Otherwise, you’d only get a few hours per day in the evening of experiencing anything you couldn’t do at home, so what’d be the point of spending home rent +hotel +travel for the week?