I don't know that Near will be out doing any "beautifying", since he has so few fucks to give, but he could be on his way to/from getting supplies. And if it's during the time where Mello is dead, he will be sad but not openly showing it because he's Near.

He at least doesn't actually hate Sharon. He doesn't like her, but generally he just thinks she's an idiot. (Idiot with good taste in art, apparently. Near, please reconsider your taste in just about everything.)