Least expensive way to plug in a microcontroller into 120V (without wall wart or batteries)
If it needs to be safe you can't get around a transformer for isolation from the mains, and you'll probably end up with the classical linear power supply:  

  

You probably can change a few things here. You say the AVR can work on 1.8V. How about the rest of the circuit? If 1.8V is enough there too you could use a lower voltage transformer. (Make sure the whole circuit can work at 1.8V. You can' use LEDs, for instance.) Digikey lists a 3.15V/600mA, but this isn't a PCB mount, otherwise it would be ideal. 3.15V AC combined with Schottky diodes for rectification give you more than 3.5V input to your regulator, which could be almost any LDO that can supply 200mA. (If you use a higher transformer voltage you'll have to use a different LDO, since this one is rated at 6V in maximum.)

This is the standard setup for a linear power supply. It may look a bit complicated, but you can't go more simple than this. The wall-wart is a nice alternative, why are you against that?