According to ESA, it's target Lissajous orbit around SEL2 is:
263,000 × 707,000 × 370,000 km, 180 day-long orbit around L2
It's the only place that suits Gaia's design constraints, to keep its solar panels pointed towards the Sun at all times, prevent thermal cycling, and keep its antenna pointed towards the parts of the Earth where it can be communicated from.
A cutaway of the Gaia space observatory showing its instruments Credit: EADS Astrium
Sun-synchronous -1° retrograde polar orbit (frozen orbit) wouldn't do, since the majority of its ground track is over the middle of nowhere. L1 wouldn't do, since the antenna can't be a part of the Sun shield then, L3 is behind the Sun, L4 & L5 still don't enable its antenna to point towards the Earth (maximum permissible tilt for its Sun shield relative to the Sun is at 15°), and higher or lower heliocentric orbits would put Earth in opposition during its 5 year mission, complicate communications (1 billion pixels creates a large data stream) and reduce total insolation needed to power the space observatory, if in higher altitude heliocentric orbit.