The phrase 'by either side of' is correct and usable in written English.
You can use it when describing the location of something in relation to two different locations or points. For example: "The old stone bridge spanned the river, with thick trees growing by either side of it."
It was not a particularly uplifting argument by either side of the debate.
According to legend Man was created in clay and you see them standing waiting for Enlightenment or Intelligence by either side of the fountain a boy and a girl, and the plant growth of the early world is suggested behind them and cast in bronze.
Meaning it can be used equally well by either side of our current American political divide.
Can be enjoyed equally by either side of the debate - the Split-ists are either the hard left who are trying to split the party.
Lewa depicts a woman delicately floating above water level, eyes askance, with her hands and arms resting by either side of her head.
It was a pretty September afternoon on the Charles River, still a lot of green on the trees and experienced collegiate boats were flying by either side of us, but the girls smiled nervously and looked around the boat at one another.
It is maintained by forces either side of the demilitarized zone [DMZ], the world's most heavily fortified border.
But Vettori wants a relaxation in the wides law when a batsman takes such an option, allowing bowlers to respond by bowling either side of the wicket.
Eto'o was denied by Gerhard Tremmel either side of half-time and it was the goalkeeper who earned the praise of Mourinho, who refused to condemn his striker.
Tendayi Darikwa and Eoin Doyle were also denied by Davies either side of the interval.
Chelsea will point to two glorious opportunities spurned by Sturridge either side of the break.
