All of the Germans I worked with were extremely polite and really were helpful in my trying to speak German, having had no previous exposure to it. I got the sense that they were kind of “offended” when I pronounced that city as you did, the American way. They went to great lengths to help me pronounce it the “right” way. I was told that the English and the Americans are the only ones who use that spelling and pronunciation because they could not pronounce the umlaut spelling in the wake of WWII.
I made up an impromptu joke in order to dispel any awkwardness at the time. After the pronunciation lesson I was given,, I told them that I could teach them to speak French in Five minutes!
How? was the incredulous reply.
Simple, I said. First say “Good Morning” in German.
They all complied.
Then I said, Place your three fingers of your right hand in your mouth and say it again.
Oddly, they all complied, and it came out as garbled gibberish.
“You have just spoken French” I said, and they all burst out laffing!...........
To do it right: On a Windows machine either use Character Map application and copy/paste or learn the alt codes, Alt+0252 on the number pad gives you "ü" (that's the only code I remember). I know it's a pain in the butt, but we are talking about Windows here.
On a Mac there are shortcuts involving the Option key then the character you want that diacritical mark over, e.g., "ü" and "Ü" are done by hitting Option-U, then typing a "u" or "U" respectively.
If you do this a lot and don't want to have to remember anything on either platform, there's PopChar, a pretty nice little utility for Mac and Windows.