Near can stand as well as walk and most likely run.
He stands when he is visiting the head of the FBI in order to start his investigation as the SPK.
He also stands up when he is studying his televisions and eventually spots Teru Mikami.
He can definitely walk and/or run, as he did so when escaping from Kira's mob (which was incited by Sakura TV).
Near (as well as Rester, Lidner and Gevanni) put on riot police uniforms with helmets in order to shield their identities as well as escape from the SPK's original headquarters.
The only way Near could have gotten out of the building was if he ran with the other members and the rest of the riot police in order to escape undetected.