What regions in Europe and other western countries would Trump win or at least do well?

[parochial boy]

Trump's approval rating in this country is sub 20%, the idea that he'd win swathes of the North is absurd. But I agree with TiltsAreUnderrated that he'd probably be strongest in places like Essex and coastal communities in the East of England, though not enough to actually win any region.

The approval relates to Trump the person from an outside perspective. Give Trump the Tory leadership and he does just a little worse than Johnson (the worse being the suburbs Johnson managed to hold for the Tories).

Yeah, even then, blatantly no. The premise of the question is how would he do. Him being who he is is someone who is nearly unanimously detested in most of Europe, and that is because of his persona, not because he likes to lash out at the EU or whatever. To say that would magically change just because he was within those countries is one hell of a stretch.

Even then, let's indulge your premise and make the assumption that Trump is in fact a completely different person, and changes huge chunks of his style and policy agenda so as to fit into a European political outlook. Even then, he is still fitting comfortably into one of the radical right parties, which, outside of maybe Italy and Flanders, and - depending on how generous you are feeling, the UK - are basically not, nor are they even close to being, capable of leading governments in any of the EU-15 + Switzerland and Norway.

[parochial boy]

Here's my 100% subjective "gut feeling" map of a worldwide Trump-Biden election. The hypothetical question is "Who would you like to be the President of the United States?" and the election is administered by each country/region's local authorities (hence some random authoritarian states having weird results that wouldn't otherwise be in line with their populace).

Now way Trump would win the East Midlands, East Anglia or Switzerland, or even come particularly close.

Exactly, before the Corona crisis, Trump already only had an approval of 12% in Switzerland. Since then it's probably dropped to 8%.

Judging by the Pew polling that was posted earlier, that would basically mean that Switzerland is pretty much the European country where Trump is the least popular. Which isn't really that surprising seeing as it's one of the few European countries that are clearly becoming more left wing.