What model should I use? I was having a discussion with my father about building an index that ranks cities as a function of multiple variables. 
For example, ranking n=20 cities based on $$$/SQFT and air quality.
I would think that regression with residual analysis is the best way to go, but there is no dependent variable.
I'm sure I'm not the first person to ask this question, so I'm looking for a waypost to direct my research.
 A: When you have variables on different scales (as in your example) and want to combine them, there are various methods. 
Taking the arithmetic mean won't work, because variables that take larger values will have more influence. One of the simplest is the geometric mean, which, for n items, takes the nth root of the product. I wrote a blog post about this measure. You could then rank by the geometric mean of each city.
Another is to arbitrarily weight each measure. After all, you are doing the ranking! Maybe some variables are very important to you and others are not. As long as you're consistent (and, if you report on your method, honest about what you did) I don't see a problem.
Getting fancier, you could do a factor analysis and see what emerged. If you have a bunch of measures for each city, they are likely to be correlated. Factor analysis can deal with this sort of thing.
I could even see a cluster analysis being useful. Perhaps there are clusters of cities that are similar and you want to rank within cluster.
