Where should I put a 3.3V Voltage Regulator?
This Is Battery Operated by a 12v Lithium Ion battery pack 


Using a linear regulator from 12V to 5V would be inefficient (about 60% power lost as heat) so I presume you used a switching regulator. If you don't know how to design one, you can get a canned DC-DC module for a few bucks from the usual suppliers. If the arduino is the only load on your battery, using a 12V to 5V DC-DC instead of a linear regulator will double your battery life, so it is much cheaper than buying a battery with more capacity.

Then, the choice of where to put the 3.3V regulator becomes simple: if it is a linear regulator, then it must be placed after the 5V switcher to exploit the switcher's efficiency. One could also use another 12V to 3V3 switcher, that depends on how much power is used on 3V3.

Where to place it on the board is another question. First, check its dissipation, and make sure it is placed in a spot with enough copper area to act as a heat sink. Heat sinking is done through the TAB pin of the package, which for LM1117 is connected to VOUT, so you will need copper area on VOUT. If you have a ground plane, and the chip dissipates enough to need good heat sinking, it may be beneficial to switch to a LDO which has the tab connected to GND. This makes the heat sinking easier. If you use a thru-hole package, whatever the TAB pin is connected to matters less, but you still need to check if it requires a heat sink or not.

Note LM1117 also has high quiescent current, so if you're going for low power, maybe not the best choice. 

Next is noise. In this case it won't matter, but if you want low noise on the output, it is best to have the regulator's GND reference connected close to the GND of the circuit that it powers.