How to boot my mac mini up when my iPod Touch is near?
On your Mac mini enter Energy Saver in System Preferences and enable the Wake for network access.  Then find an app in the App Store that does Wake on Lan, this is one such app - http://itunes.apple.com/us/app/inet-wol-wake-on-lan/id318696675?mt=8 that I found during a search.  There might be others that fit your needs better.