God is an Astronaut is quite unique in the fact that they rely on instrumental compositions in their post-rock. It is pretty much impossible to find something that follows in the same vein, although I know a few that are close.
Ef, one of the veteran bands of the post-rock scene has made a few almost instrumental songs that sound like God is an Astronaut, if the band members were younger, more fragile, introspective and wrote all their songs on rainy days.
Here is the most fitting song: (Note, it stops being instrumental at around 5 minutes)Year of No Light, a French band mostly relying on guitars for the grandiose atmosphere that they produce. Their song Perséphone is long, dreamy and full of splendour.
Thränenkind is a German band, normally known for their post-black metal have also made a instrumental piece which is definitely worth a listen. It is a very slow journey and quite anticlimactic, so save it for a rainy day.
Other bands worth mentioning:
Ethereal Beauty, especially with their song "The Sun Shines Tomorrow"
Explosions in the Sky, pretty much any of their later work.