There is a soccer ball you can play with in the Tower, by the crates in the left area.
There is also a purple ball you can play with in the Tower, which descends very slowly when knocked into the air. It can appear at one of two places: on a table beside Master Rahool's shop, or to the right of the Bounty Tracker.
During the Mars Strike mission, head around the back of the command center and look up at it from an angle. It resembles the Master Chief, from the Halo series previously owned by Bungie.
In the first cutscene, the Destiny logo is printed in the astronaut's footprint.