By the way, make sure that the 10uF on the regulator’s output is a Tantalum capacitor; that regulator needs a specific ESR and calls for Tantalum. The 0.1uF Ceramic and 47uF Electrolytic aren’t required, but they will help keep noise out of the system. (Different size capacitors respond to different frequencies, just like antennas. Those are two common sizes of bypass capacitors, so between all three you should be set!)
As for using that on line voltage, unfortunately, no. 120VAC is far too high for a linear regulator. This is why old school AC Adapters were so big and heavy, they had to include a transformer to bring the voltage down. Modern adapters are the product of very fast and robust power transistors. Though, that’s not to say that they don’t still use transformers. Most higher quality adapters will use a synchronous isolated flyback transformer design for the output voltage regulation. (Essentially you convert the incoming AC into High-Voltage DC with a rectifier, run it through a MOSFET to reduce the voltage then run the chopped DC through a tiny flyback transformer (which converts it what’s essentially low-voltage AC) before finally putting it into a backwards rectifier (which basically means when the transformer is being powered the diodes block). It’s really cool technology!
Here’s a reference design for a 1"x1" 5V/2.1A adapter: http://www.ti.com/tool/pmp8286
Here’s what’s inside of an Apple Charging Cube: http://www.righto.com/2012/05/apple-iphone-charger-teardown-quality.html
Anyway, what I would do if I were you is just get a small cube charger like that (Samsung has one that retails for about $10) and solder AC wires directly to it, then cover the exposed prongs with a couple of layers of heat shrink tubing. This way all the hazardous stuff is safely enclosed. I think that would be safer than taking apart an adapter. (Seriously, be careful though! Live AC is not a joke!)