Django + postgreSQL: find near points
You're probably right, PostGIS/GeoDjango is probably overkill, but making your own Django app would not be too much trouble for your simple task. Django offers a lot in terms of templating, etc. and with the built in admin makes it pretty easy to enter single records. And GeoDjango is part of contrib, so you can always use it later if your project needs it.
For my app, I need to determine the nearest points to some other point and I am looking for a simple but relatively fast (in terms of performance) solution. I was thinking about using PostGIS and GeoDjango but I think my app is not really that "geographic" (I still don't really know what that means though). The geographic part (around 5 percent of the whole) is that I need to keep coordinates of objects (people and places) and then there is this task to find the nearest points. To put it simply, PostGIS and GeoDjango seems to be an overkill here. 
I was also thinking of django-haystack with SOLR or Elasticsearch because I am going to need a strong, strong text search capabilities and these engines have also these "geographic" features. But not sure about it either as I am afraid of core db <-> search engine db synchronisation and hardware requirements for these engines. At the moment I am more akin to use posgreSQL trigrams and some custom way to do that "find near points problem". Is there any good one?