How do I change a neighbourhood point to an area

Draw a new area (closed way) and tag it as the node (point) is tagged (the editors Potlatch2 and JOSM offer copy&paste for tags – which is helpful if there are many tags to be copied over). Afterwards delete the node (alternatively, as I would do it, you can use the node as a corner node of the area way). Enter an explaining changeset comment on save (so people looking at the history of the closed way know that the data is sourced from the deleted node).

See our wiki about our object types and area (which is simply a closed way). And about neighbourhood (area could be seen as problematic if the real-world edges of the neighbourhood would be not clearly defined).

Another option is to make a relation for the neighborhood boundaries. For example, if the neighborhood boundaries are mostly along streets, you can use the streets as relation members rather than having redundant and overlapping ways. The relation would probably be tagged type=boundary with the name. To extend the tagging, you could tag place=neighbourhood, but if it is an official boundary (and depending on if there's any local standards used), I'd suggest boundary=administrative and admin_level=* The relation could also keep the node, and have it take the admin_centre or label role. More info on this method on the wiki: http://wiki.openstreetmap.org/wiki/Relation:boundary

Note that rendering of this sort of data is still real hit and miss. For example, if you use relations like I've tried (see for example Relation 3323777), "Standard" Mapnik will have a label in the center of the relation area, MapQuest and Humanitarian at the label node, and Cycle and Transport don't support at all.

For place=neighbourhood, generally only MapQuest and Humanitarian render it consistently in my experience. (and for completeness' sake, they all render place=suburb to one degree or another)