If moons about our gas giants are an indication, the moons would likely be tide locked.
This makes for some interesting differences in cartography.
On earth's globe there's two non-arbitrary points: The north and south pole. And there's a non arbitrary great circle: the equator.
But for a tide-locked world, there are 4 non-arbitary great circles and 8 non-arbitrary points:
Circle containing near point, far point, south pole and north pole
Circle containing leading point, trailing point, north pole and south pole
(In this image I called the leading and trailing points the Left Ear and Right Ear.)
I would expect the tide locking to have a huge impact on evolution of the inhabitant's religion and culture.
For example I would expect the near point to become sort of a Mecca. They might build a temple on the the near point. Viewed from this temple, the gas giant would hover motionless at the zenith. Or the moon has some obliquity, the gas giant might trace an analemma with the analemma's center at zenith.
If this gas giant is like the giants in our solar system, it will likely have a whole family of moons, many of them near planetary size. It would be like a mini solar system. But travel between moons of a gas giant could take place at a much faster pace than travel between planets. Launch windows between destinations would occur on the order of weeks apart vs years apart (for example earth to Mars launch windows occur each 2.14 years). Trip times between moons would be on the order of weeks (Hohmann trip time between earth and Mars is about 8.5 months).
An elevator could be built from the moon's far point through the gas giant/moon L2 point and another elevator built from the moon's near point through the gas giant/moon L1 point. If such elevators were built on each moon, the civilization could travel between moons using virtually no reaction mass.