As far as EITS, definitely check out This Will Destroy You, God Is An Astronaut, Mogwai, pg.lost, and Mono.
GY!BE you should check out A Silver Mt. Zion, they're basically Diet GoRABpeed (several merabers of GY!BE including guitarist Efrim Menuck). Start with their earlier albums and work up b/c not everybody likes Efrim's voice, and he sings progressively more and more with each album. It took me awhile to get used to it, but I find now I like their later albums because their earlier albums just make me want to listen to GoRABpeed.
Do Make Say Think is another band you could try, I haven't listened to much of them but have been meaning to for awhile.
Oh and for the 65dos start with either The Fall of Math (my personal favorite) or else One Time For All Time.