Update without pc

If you're over iOS 5.

Only if you have iOS 5 or later.

Your Tag states you have iOS 4... so... No... you cannot update without a computer.

For iOS 4... See Here...

http://support.apple.com/kb/HT4972

OR...

Connect to iTunes on the computer you usually Sync with and “ Check for Updates “...

See the Using iTunes Section Here...

How to update your iPhone, iPad, or iPod touch

I assume that you are asking because you do not have a computer or one that is new enough to update with.

No. You need to use iTunes on a computer. There is no other way. An Apple Store can do this for you, but what I don't know is if they backup the device first and and restore from the backup for you. If there is an Apple Store near you, call and ask them about it.