Is it correct to say ''For a long time I haven't visited Tom'', without continuing the sentence? Isn't there any grammar rule to state that the order should be : ''I haven't visited Tom for a long time''?
It doesn't sound right to me. I feel like I need and affirmative sentence to follow ''For a long time'', if I don't give an explanation of my actions.
Maybe I'm just tired, It's almost 2am here. Thank you.
Adverbial phrases can generally move around English sentences freely. In cases like your sentence, the phrase for a long time can modify only the verb (here, have visited), so beginning or end, both positions in this case are available to mean the same thing. This lets you write sentences like
[1] For a long time, I haven't visited Tom, my older brother and the tallest of my siblings.
In [1], the compound appositive precludes other locations for the adverbial phrase, so it's a good thing the beginning of the sentence is available for it.
Note that sometimes, moving the adverbial phrase changes the meaning:
[2a] For a long time, I haven't visited Tom, who has been a good friend.
[2b] I haven't visited Tom, who as been a good friend for a long time.
[2a] and [2b] mean different things.
