I have a road layer of a country. What method or plugin would you suggest, to find a single point furthest from any road
(but as you can see, there is a coastline, so points in the sea can't count)
The road layer looks like this:

First you need to rasterize the layer and then you can use proximity analysis from the GDAL Tools plugin: Raster > Analysis > Proximity.
More information can be found in the following related answer: Calculating distance to points in QGIS
in that case: single point furthest from any road (but as you can see, there is a coastline, so points in the sea can't count)
– normis Dec 16 '13 at 10:22