"your"
there are so many expats here of various nationalities - ages - denominations and so-on that you would find no problems there. Nor should you find problems getting an apartment or a bed.
You're better off within Investment Banking if you come over with UBS. Why? If you're not in IT, there are more foreigners I believe in the IB area than elsewhere in the Swiss business side.
Best bet I'd say is get onboard with UBS WM in the US and do an internal transfer - then you get full UBS buy-in for the move, the permit, apartment, etc. Ask about that too - I believe they call it International Assignee.