TNet uses a "channel" system that can be used (and seems to be designed for) your needs. You split your scene into however many regions you feel is necessary, and then as your player travels around the scene they join / leave channels according to the region they're in. Not only does this effectively result in proximity-based network updates, it also completely cleans up objects from channels that you leave. Objects belong to channels, so when you're no longer in that channel the object gets destroyed, and when you join a new channel all objects belonging to that channel are automatically created for you. This reduces GPU load as you won't have to be rendering any distant complex objects at any LOD if they're outside your region, and it also reduces CPU load as there won't be any MonoBehaviour's executing outside your region.
Reference (straight from the horse's mouth, so to speak):
http://www.tasharen.com/forum/index.php?topic=15211.msg66256#msg66256Though I should add: splitting your scene into these regions - and joining/leaving channels based on which region you're in - isn't built directly into TNet. Because there can be a million different types of scenes (flat, spherical planets, something more abstract, etc) it'd be impossible to handle automagically, so you'll have to figure out how to split up your scene, how to determine which region a player lies in at any time, and then join/leave the appropriate channels.