Actually, Oatbarton is the only location that is definitively identified in canon as the belonging to the Northfarthing. We can be confident that Hardbottle also lay in this area because, while not stated in any canonical source, Tolkien confirms this in his guide for translators. Long Cleeve is a less definite case, but there are various clues, including its connection with the North-took family, that point to it being within the borders of the Northfarthing.
2
The northern areas of the Shire's Northfarthing are nowhere mapped in detail, so some elements of this map are necessarily conjectural. In particular, the location of the river Norbourn and the Greenfields region are based entirely on textual descriptions. The upper course of the Water is also unknown (it is assumed here that it had its sources in the slopes of the Hills of Evendim) and the northern extent of Bindbole Wood is not definitively established.