Hello everyone... Should I use #12 wire and 20 amp Arch fault breakers in the living room and bedroom area recepticles since 120v air conditioners will be using these at times?

That would be a wise suggestion.

However, installing dedicated circuits and receptacles for any AC unit would be much better.

Thanks tkrussell for your answer. I think I'll take your advice and run dedicated circuits to the outlets using the air conditioners. I have another question... Do I need to use dedicated GFCI at the washing machine?

A washer would not need a GFI, unless, it is within 6 feet of a sink.

Remember, even the AC circuits will need Arc Fault protection, assuming the circuits will be 120 volts. If 240 volts, then Arc Fault protection will not be needed.