"visitor side" is correct and usable in written English.
For example, you could use it in the following sentence: "We stayed on the visitor side of the baseball stadium."
Between falling prices, secondary-market commissions, and the fact that home and visitor sides of the field were assigned by the B.C.S. weeks after I'd bought my tickets — leaving me stuck with vastly less valuable Alabama seats — my plan to cover my costs through scalping had gone up in smoke.
On the visitors' side, Mussina was not laughing.
Stands on the visitors' side of the field disappeared in the storm.
At that moment on the visitors' side, Paul O'Neill was playing a spirited game of cribbage.
The girls returned to the empty bleachers on the visitors' side of the gym, munching on candy and popcorn.
Around that time, the condemned bleachers on the visitors' side were razed, but the rest of the facilities remained, becoming increasingly dilapidated as the years passed.
But I couldn't believe what I saw during the fourth quarter: two sets of four tickets, eight rows apart, on the 35-yard line of the visitors' side.
At about 4 p.m. Monday, Suzuki, wearing a dark blue suit with gray pinstripes, walked down the hallway from the Seattle clubhouse over to the visitors' side, adding victories and vaulting upward in the standings with each step.
He joked that his top assistant, Gene Keady, had to remind him they were sitting on the visitors' side of the court when Lavin appeared to hesitate in front of the home end.
