Under the assumption that buildings are quite a bit higher than their surrounding environment, you could perform a cluster analysis on your height data. Depending on your data, this could lead to several clusters: high buildings, low buildings, surrounding landscape. There are some issues, for example, a high tree might be just as high as a low building.
Alternatively, you could perform some kind of (un)supervised classification in which you could use the height information and possibly other source of information such as not only the height information at the current location, but also the surrounding height.
Once you've determined which area of the map could be classified as city, or urban area, you could provide statistics such as mean and variance to describe the height and variations in the height.
Which analysis works well also depends on which data you are going to use. Very high resolution LIDAR data supports other analysis than very coarse SRTM images. Also take care that some height products have compensated for buildings as they where not interested in them.
Then there is the question of how to do this kind of analysis. I use R and other high level programming languages to do this. These tools have a steep learning curve, but provide ultimate flexibility. I don't use GUI tools such as ArcGIS, so I'm not up to speed how these support the kind of analyses I suggested. You could also take a look at QGis, GRASS, or SAGA. These are open source (and free) GIS tools.
Best Answer
I ended up with this solution with PDAL and GDAL:
First I used liblas to create LAS containing only ground points. Then I used PDAL similar to the "Basic Example" but with
output_type: maxto create a DTM from the terrain LAS and a DSM from the original LAS.Then just gdal_calc.py with these to elevation models to get a DHM.