According to List of highest towns by countrythere are towns or permanent settlements as high as 16728 ft (La Rinconada, Peru). I doubt this list is exhaustive.
Which is the highest city you have visited, passed through or slept in? I as going to title this thread "Highest sleeping altitude". Then I realised, this is FlyerTalk. Just about everyone has slept at altitudes higher than Mt Everest.
I have passed through many high altitude towns whose names I don't even know. They are all in the Himalayas. The highest towns I have slept in are around Bhojvasa-12400 ft (Google Earth) Badrinaath-12300 ft (Wikipedia) and 10,200 (Google Earth), and Kedarnath-11600 ft (both Wiki and Google Earth).
Did you experience any altitude effects? I think I didn't. I did forget my back back or money bag a few times, but always got it back. Confusion maybe?
Highest city I have slept in was La Paz, Bolivia, at 3,640 m. Got quite ill from altitude sickness, and had to leave and head down to Chile to escape the altitude.
The highest I have slept is Mawenzi Tarn on Mount Kilimanjaro at 4,330m. I got awfully sick with High Altitude Pulmonary Eadema, and had to be evacuated off the mountain in a stretcher.
After that, I decided I wasn't going to try any more high altitude stuff. I decided not to get above 3,100 meters.
Sorry to hear about your altitude sickness. I travelled by road, which probably acclimatised me better. On my last trip I took about 48 hours to go from a few hundred feet to 12000 feet. I did quite a bit of walking during my halts. Once there, I walked a lot too. I was a bit concerned about the low partial pressure of oxygen as I use a CPA.P The worst was going to bed without heat. I would cover my head, CPAP is great for that as you can still breath with your head covered. It was nearly two hours before I felt cozy.