rich guy who has been neglected by his family his whole life but his best friend takes care of him

At a Distance, Spring Is Green (the bromance part but it takes a bit to get there, though)

Also maybe...

• Golden Blood (it's quite a bit like Where Your Eyes Linger).
• Stay with Me 
• Bokura no Shokutaku (I'm not sure if he's rich but he's distant from his family and finds love and family warmth with the other ML and his family).