Just enjoy it. The Touch G4 has a pretty decent DAC chip, and sounds good as a portable. If you want to avoid the in-built amp, get a LOD (line out device/dock), and a small portable amp - either the Fiio E11 or a Cmoy are good starters. You can go a lot higher up the chain depending on budget.
Use higher bit-rate MP3 or AAC files (don't worry about lossless - unless you've got 'golden ears', most people find very little difference between a 256aac / 320mp3 file and lossless on a portable). If you're uncertain. set-up foobar with the ABX comparator, and test yourself. Almost all of the time I cannot tell the difference between well recorded 256aac and well recorded ALAC. Best to know yourself - and then you've got a lot more space available for music.
Get the equalizer or equ app (they are both cheap). The equalisers on both apps are miles better than the native Apple ones.
You haven't listed your cans - so it's hard to say whether an upgrade would help.
FWIW - my portable / tranportable set-up consists of:
Ultraportable = Touch G4/IP4 (I have both) -> Brainwavz B2 (straight from the headphone out)
Portable = Touch G4/IP4 -> LOD -> E11 -> MS1i (woodied)
Transportable = Touch G4/IP4 -> LOD -> PortaTube -> HD600
Ignore the people who say the G4 / IP4 have crap quality. I've owned Cowons and my current G4 Apples - and IMO they are pretty much on par.