With 54% of the world's population urban in 2014 it is important to assess the sustainability of cities and find systematic ways of improving it. In this paper the model SAFE (sustainability assessment by fuzzy evaluation) that was first developed to define and measure the sustainability of countries, is modified to assess the sustainability of cities worldwide. Overall sustainability is a function of two main inputs, ecological and well-being. The ecological input depends on the state of air, land and water and the well-being input on the state of the economy, education, health and civic environment of cities. SAFE uses 46 basic inputs to rank 106 cities according to sustainability. The number of inputs can be changed according to need. A sensitivity analysis identifies those basic inputs or indicators that affect sustainability the most. If such inputs are improved, the sustainability of cities improves the fastest. It turns out that European cities occupy the highest ranking positions whereas African, Asian, and South American cities the lowest. Waste generation and GHG (greenhouse gases) emissions are the main problems for cities in the developed world, whereas crime and poverty are the main problems in cities of developing countries.