Under 3 hours: stay in the terminal
With a short layover, the airport itself is the whole plan — KIX has a reasonable range of restaurants and shops airside, and the connecting Aeroplaza building on the landside has more options if you've already cleared immigration. Coin lockers are available for stashing a bag if you want to move around unencumbered.
3 to 6 hours: Rinku Town
With a few more hours and if you're already through immigration, a short train ride across the bridge to Rinku Town gives access to a large outlet shopping mall and a proper meal away from airport pricing, with easy return access to the terminal in a few minutes by rail.
6+ hours: a short trip into Osaka
With half a day or more, the Haruka Express or Nankai Rapi:t can get you into central Osaka in under an hour each way, leaving a genuine window to see one or two things — Osaka Castle's park, or a walk through Dotonbori — before heading back. Build in generous buffer time for the return journey and airport security, and keep essentials in a carry-on rather than checked luggage if this is the plan.
If your layover involves re-clearing immigration and security, check your visa situation for a short landside visit before committing to leaving the airport — rules vary by nationality and by whether you're transiting internationally.