We spent three days at the Villas at the Disneyland Hotel last week and rope dropped three consecutive mornings. I found the exit entrance between Adventure and Frontier Towers to be the most direct route to the new Downtown Disney Security entrance.
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You walk out the gate, across the road and there is the entrance. Very convenient.
Sunday June 23 we got there around 6 am and were the third family in line. Monday June 24 we meant to get there later but arrived around 6:15 am and were the second family in line. Tuesday June 25 arrived around 6:05 and were first in line. Only a handful of families between 6 and 6:15 each morning. About 20 to 30 families by 6:30 and too many to count by 7:00. Very few people coming from Pixar Place or the parking lots. Most people came from hotel via the Sorcerer's Hat. I didn't pay attention to the time security actually opened but it was never at 7, always a bit after. You know it is nearly time when the dog comes on duty.
At opening there were between 3 and five lines open. We spend less than one minute going through security and then began the walk to the park gates. We arrived at the park gates around 7: 18 am and were about the fifth family in line each day.
We left the park each day around noon or one. The exit gate changed sides each day. Returning to the parks around 4 or 5 pm we usually only one or two groups ahead of us with about 3 to five lines open.