I saw this earlier as "Я здесь живу." Is there any preference as to where "здесь" falls grammatically?
There's no difference between the meanings, both mean the same thing - "I live here." The only difference can be WHAT EXACTLY you want to point out by your sentence, therefore on which word you put the stress. If you want to point out the exact place where you live then you'd say "Я живу здесь." (the stress is on здесь). And if you want to mention what you do here, you'd say "Я здесь живу." (stress is on живу).
I've come to distinguish the two by knowing that Вот translates to "here is" as in вот мой кот, Кирил whereas здесь means just simply "here" usually used to demonstrate location such as кого здесь ты знаешь?
If you really wanted to be fancy, you could say Я здесь живу. Вот мой дом. "I live here. Here is my home"
Hopefully that has cleared it up a bit