Apple will exchange your iPod for a refurbished one for this price. They do not fix yours.
You can go to a store or send it to Apple. See:
A third-party place like the following maybe less. Google for more.
Replace the screen yourself
Out-of-Warranty ServiceIf you own an iPad that is ineligible for warranty service but is eligible for Out-of-Warranty (OOW) Service, Apple will replace your iPad with an iPad that is new or equivalent to new in both performance and reliability for the Out-of-Warranty Service fee listed below.
A $6.95 shipping fee will be added if service is arranged through Apple and requires shipping. All fees are in US dollars and are subject to local tax.
iPad model Out-of-Warranty Service Fee iPad mini $219 iPad 3rd, 4th generation $299 iPad 2, iPad $249
Certain damage is ineligible for out-of-warranty service, including catastrophic damage, such as the device separating into multiple pieces, and inoperability caused by unauthorized modifications. However, an iPad that has failed due to contact with liquid may be eligible for out-of-warranty service.Apple reserves the right to determine whether or not your iPad is eligible for Out-of-Warranty service. Replacement iPads have a 90-day limited hardware warranty or assume the remainder of your standard warranty or AppleCare service contract coverage, whichever is longer. Please see the AppleCare+ for iPad and Apple Repair Terms And Conditions for further details.
This is the iPod touch forum.