Я сейчас нахожусь в Дно
Я сейчас нахожусь в Дне ?
I am especially curious about how the natives of the city go about this matter.
Nouns are not conjugated, they are declined.
City names in Russian are declined with the exception of some foreign names, in which case the rules are quite complicated -- see http://www.gramota.ru/spravka/letters/?rub=rubric_90 (in Russian). So the correct version is "Я сейчас нахожусь в Дне".
In my opinion, when in doubt whether you must decline a city name or not, safer would be to say "в городе X" (vs. just "в X") and not decline the name. The reason is that it's a pretty common error for Russians not to decline city names at all if prepended with "город[-е/-а/etc]".
Дно is recognized as native word, so it should be declined. Even more – Russians will doubt for a moment before saying в Дне, because на дне is more probable and "natural" way of saying this common word.
Сан-Диего and Сан-Франциско are recognized as foreign words, so they shouldn't be declined. Some common non-native words like пальто, бюро, кимоно – also.
Transitional case are native toponyms like Домодедово, Шереметьево. They used to be immutable in Soviet times (don't know why), but currently more people tend to decline them: в Домодедове for example.
Think of it like when Russians got some new word from other language, they don't know what to do with it – what gender to use, how to decline. After some time they may adapt it and start to decline it as usual Russian word.