Forbidden Planet is on Burleigh Street, which is just behind the Grafton Centre shopping centre - it's actually recently moved into a significantly larger unit. Aside from that, as NormanicGrav said, your main avenue for anime is HMV, which is only about a 2 minute walk from Forbidden Planet on Fitzroy Street (funnily enough, if you exit the Grafton Centre from the doors nearest Next, you'll come to a fork in the road where you can either go to Burleigh Street or Fitzroy Street). If you're looking for blu-rays in HMV, be warned in that all the blu-rays are stored in the giant generic section...making finding them quite difficult xD.
For manga, Waterstones is near the market square, as is WH Smith. WH Smith tends to only stock Viz Media UK titles though - Waterstones has quite a large selection though (I was only in there yesterday, they have everything from Attack On Titan, to Naruto to Puella Magi Madoka Magica. They did have WataMote but oops, I bought the last one on display xD).