^ beat me to it
The first queen move usually wants to do two things:
1. Move off the back rank to connect the rooks and
2. Go to a square where it wont be forced to move again later from being attacked.
#2 is for any move really, but with the queen it's not so easy. On any advanced square e.g. on the 4th or 5th rank nearly any pawn move or natural developing move from the opponent would force the queen to move again. Because the e and d files can often be opened the queen may later be forced to move when an enemy rook moves to that open file. Also the squares e2, d2, d3, e3 (and the equivalent for black) are usually left clear for fast and easy development of minor pieces, especially the bishops. c3/c6 and f3/f6 are usually reserved for a knight or pawn. So that basically leaves us with c2/c7 or b3/b6 and sometimes a4/a5.
Sometimes, however, the c file will be opened later and both players avoid putting the queen on c2 or c7. In this case often the queen ends up on d2, d3, e2, d3 (after the bishop is developed). Another often seen development is to e1/e8 to go to the kingside and aid in an attack.
This is something I actually used to wonder myself when I was first trying to learn chess strategy, and I think it's an overlooked question!
Because of the pieces/pawns in the center, the queen usually cannot/does not want to enter the game there.
That pretty much leaves the squares a4/a5, b3/b6, and c2/c7. The queen should move to one of these squares in order to connect the rooks and complete development.
Of those choices, c2/c7 is typically the safest and less exposed square for the queen, though one needs to be careful about Nc3-b5/d5 or ...Nc6-b4/d4.
The best advice I can give is to bring the queen to the safest square you can where she will be able to easily jump into action later.