Smallest AC to DC converter
The smallest might well be a cellphone charger such as this one:


From this site

You can either embed the entire charger into your enclosure, or if you are comfortable and qualified for working with mains voltages, extract the actual charger circuitry inside and embed that. 

Such chargers typically output 5 Volts DC with line isolation, so the output can be used to directly drive the Vin line of the Arduino board, rather than going through the 7-12 Volt DC input and the on-board regulator.