Hitomi Kanzaki is a typical high school girl, with typical problems, but when a vision of a young man battling a dragon becomes a reality, her life changes forever. Drawn into a strange vortex with the swordsman, Van, Hitomi is thrust into the strange world of Gaea. Van must learn to master the suit of armor, Escaflowne, before he and Hitomi are crushed by the ambitions of the Empire of Zaibach. Van and Hitomi will encounter both allies and enemies in an effort to unlock the secrets within Escaflowne, and Hitomi's heart, stirred by love and adventure, will, at times ache with sorrow. But why was she sent to this world? Her journey has just begun!
Escaflowne was a big part of my anime childhood ritual, it's a good mixture of mech and some of the girlier aspects of anime so would fit well in the robot/mech slot, perhaps in place of Gundam or alongside it. It was shown in full dub on Fox Kids in the UK, I'm not certain where in the U.S, but it's definitely available. It has a strong storyline and VA's we all already know from Gundam Wing. I'm genuinely suprised it doesn't seem to have been suggested before. I think it has a wide appeal base which is difficult to attain in a lot of animes.
Episodes run at around 20 minutes so it fits the time constraints as well.