There are no other ideas. You need a computer to update the iPad. There is no alternative. As for the songs, without updating to iOS 5.1.1 you do not have the ability to remove the songs without unsyncing them from iTunes which once again means that you need a computer. In iOS 5 and up, you can delete the songs directly on the device, but not in earlier iOS versions.
You can take the iPad to an Apple Store and they can update it for you, but you will lose everything on the iPad unless you can back it up on another computer, restore from that backup and then download all of your content again.
Bottom line - you must have a computer and do this through iTunes or you are stuck.