Go to the app store and go to the top free apps section.
Aside from that, you can get AppOfTheDay, which will give a link to one free app per day. Something like AppShopper will also show free apps, and there is likely a bunch more.
Keep in mind that many games are starting to be unavailable for the iPod touch 4 (it is 4 and a half years old and 2 iOS versions behind), but some still exist.