I'm pretty late. Not sure if you've learned this already but I'll answer just in case. I'm not a native, but if you want to say "no longer" I would opt for «Я теперь не в Москве». Теперь means now in the sense of "as opposed to before;" it's used when things have changed- "It was this, but now it's this." In our case, "I was in Moscow, but now I'm not --> I'm no longer in Moscow --> I'm not in Moscow now."
Simply because this sentence uses сейчас I'm tempted to think there is no change from a previous condition is implied; rather, it's just a simple "I'm not in Moscow at the moment."
Native speakers feel free to tell me why I have no idea what I'm talking about.
My thoughts exactly. "Now", "yet/still", "already", "no longer" all describe what is happening now but are quite different in how they place "now" in relation to what WAS and what is about to come.
In Russian, "already" is rendered with уже, and "no longer" is expressed with уже не (=already not) or больше не (lit. "no more"). I guess, теперь не also has a good overlap with this meaning in some situations.
The meaning is rather close but it is not expressed the same way.
It is similar to how "Tom is not available" and "Tom is not available right now" are not quite the same (for one, adding "right now" suggests he may become available soon). If they were, English would not have the word for "now".