I haven't done it (and never will, since I'm now retired), but I'd have jumped at the chance assuming I wasn't locked into always needing to be available for contact during the US workday. (In that case I'd have opted for Central or South America.)
What I have done twice is spend two weeks taking 3 or 4 hours of language lessons per day, which also involved some homework. So it wasn't a full day's work, but I had substantial time commitments that made the experience different from being on vacation. I found the situation had definite pluses. Aside from the obvious deep-dive into one location, it was relaxing not to feel I had to fill every possible moment with some sort of tourist activity. I could plan to go to one small museum a day and not feel lazy. I also nearly always managed to have one nice restaurant meal per day; when I'm in full-tourist mode, I too often prioritize sightseeing over food and settle for something casual and not so interesting.
I agree that selection of location is key. I'd want either a major city (one of the capitals, Barcelona or the like) or a major transportation hub with a wealth of quick side-trip options. In the latter category I commend Nice to your attention. That was the location of one of my language stays, and it was ideal: Six art museums in town, an historic district to explore, a nice market, cheap rail service to whisk me to any number of places along the Riviera, and bus service (slower) for visiting a bunch of inland towns. Lodging rates, at least in May 2017, were surprisingly reasonable.
My other language lessons were in Orvieto. I really enjoyed Orvieto, but for mixing classes and sightseeing it was a bit too small and awkwardly located for two weeks. It was hard to leave town on a day when I had lessons.
I will say that for me (not naturally an early riser), it worked best to have lessons in the morning so I was free later in the day. Without the imperative of getting up and being somewhere at 9 AM, I tended to fritter away most of the morning and do nothing except have lunch before an afternoon class. I don't know how much freedom you'll have in the scheduling of your work hours.
Planning this escape for the period when days are longest might somewhat reduce the impact of having to be available to your colleagues during their US working hours, if that's something you have to deal with.