You can't really visit the royal palace.  It's interesting from a cultural point of view but don't expect to be let in. However you can ask a Taxi to drop you by the entrance of the walled section and walk in. It's a bit impressive but the guards do let you in, especially if you do look like a tourist (this is the time to have camera and all other touristy gizmos on). It's an extremely nice stroll through the garden. You can walk for a solid hour up to the real Palace entrance, even take photo, and exit from another entrance.