Resorts World Manila is a Casino/Maill right in front of NAIA Terminal 3. It is relatively new because the stores are not yet open. One of my friends work at Resorts World as a Poker dealer.
If you are taking Public Transport, the easiest way is to have access to LRT/MRT on Taft Avenue cor EDSA first. Once you get there, you need to look for the shuttle that goes to Terminals 1-2-3. The shuttle station is hard to find but it would be on the North bound side of EDSA together with the buses going to Batangas and the Jeeps going to Nichols.
The Shuttle Bus fare is 20 pesos only. It would take you directly to Resorts World in a matter of minutes. Just be patient.
Going back to MRT/LRT is no easy task as well. The fast way is to ride the Jeepney that goes around Nichols, alight at 7-11 where all the Jeeps going to Baclaran awaits (but do not ride these jeeps). Walk a little bit farther. You will see 6-seater trikes that would take you to EDSA. You may then walk to the MRT station if you must.
So there you have it. I wish you goodluck on going to Resorts World.