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.
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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.