No, I never completed Gau's list I'm afraid... The Veldt theme gets on my nerves after a few days of listening to it.

Definetly head out and do a few side quests. Now's a good time to collect Strago's Lores', collect Mog's Dances, and start teaching everyone all the healing magic you have. It will come in very handy later. Also, a small hint... after the events following the battle with Atma, be patient when leaving...