Thanks for all your inputs. As it turns out, I decided to put the new
outlet where the old one was. It didn't make sense to put the outlet
behind on the switch box, and I did not want to put under the window
in case we put a towel rack. So the only logical place was where the
old one was.

I did run a new 20A circuit. The only other loads will be the fan
(48W) vanity light (200W) , and shower hi-hat light (65W).

Speaking of the shower light, because I had to put it on a GFI, I ran
the 20A feed first to the switchbox, then a ran a jumper to the GFI
outlet, then I ran another jumper from the GFI back to the switchbox
( LOAD side of GFI) so the shower light switch will be protected. Of
course I could have just saved some trouble by putting a GFI breaker,
Or run the feed first to the GFI outlet, then run a LOAD side jumper
back to the switchbox, but I did not want the vanity lights and fan on
GFI, so this seemed like the only wiring solution, right?