First of all Mikhail Krug belongs to so called genre of 'блатные песни' = 'songs of/for criminal underground'. You need no to belong to criminal to listen them, but they are not appropriate for central TV often, for example. This one is some kind of neutral.
'Девочка-пай' (devochka-pai) is reverse of 'Пай-девочка' which is 'good girl' in sense of child obeing parents, living good and right life of innocence and so on.
This song is about relations between criminal guy with 'good girl'.
I have no time to do complete translation, so there is translation of refrain. I divide text by rhythm.

Как (pause) было тепло // It was so warm
Что нас с тобой // so you and me
вместе свело // came together

Девочка-пай // good girl
рядом жиган // with rogue
и хулиган // and hooligan

В нашей Твери // Our Tver (city) don't know // keep in mind - 'our' means 'criminal Tver'
нету таких // such a girls
Даже среди // Even amongst
шкур центровых // the chicks/bitches from central district

Девочка-пай // Good girl
ты не грусти // don't be sad
и не скучай // and don't be bored // in russian can be perceived as 'don't miss me' because of context