I'm so glad you got her back!
***I literally just went through this with my 4 year-old Quaker Parrot last Friday night around 5:30 p.m....I opened up my sliding-glass door to let my dogs out into the backyard, Lita was on my shoulder, and for whatever reason, I still don't know why, I wasn't thinking about her being on my shoulder...It was raining lightly and I stepped one step outside onto the patio step to move a potted succulent plant out of the rain, the neighbor's dog barked at my dogs, and she got spooked and flew off of my shoulder forward, I screamed for her, she tried to immediately come back to me but instead was too high and flew right over the roof of my house towards the front yard/street. I ran through the house to the front and the heaviest rainstorm we've had in Central PA in decades suddenly started...Lost her for about 20 minutes until the rain stopped, then called to her and found her in what I thought was the tallest tree in the world in my back-side yard, but she wouldn't come down. Kept talking to me, I could see her, she danced with me, etc., but could not come down...She spent the night in that tree, I put her cage and her Play-Stand outside and in-front of the tree she was in, but a bit aways so she wouldn't be flying straight down to the cage, but rather forward and down to it...At sunset she and the wild birds stopped talking to me for the night. I got didn't sleep at all, and at 4:30 a.m. went back outside to find her in again what I thought was the tallest tree in the world in my neighbor's backyard...Move her cage and stand to my neighbor's deck and above-ground pool deck, and sat and talked to her for over 2 hours, but she just would not come down...Then a Crow came and chased her out of that tree, out of the backyard, and over to a different street...I then found her again (thank God she's BLUE and not Green, lol)...She called right back to me and then the Crows, yes CROWS, 4-5 of them that were 3 times her size, again went right after her and were about a foot behind her flying, and I lost her...I looked for another 2 hours, calling to her, nothing...Went home, posted online EVERYWHERE, ate something, then went back out to look for her again around 1:30 p.m....I thought the Crows had killed her/eaten her, and I was crying the entire time I was walking around and calling to her, looking for blue-feathers on the ground as I was 100% certain they had killed her and ripped her apart...Then around 3:00 p.m. I heard her calling back to me again...She was in a Pine Tree in someone's front yard about a mile away from my house, I didn't know them but they too helped me just like your neighbors did...People really can be amazing...They got me a ladder, then an extension ladder, nuts, orange juice, etc. But then she flew to what REALLY WAS THE TALLEST TREE IN THE WORLD finally, it was a towering tree and she was right at the top, I couldn't see her but I heard her. So I sat in this person's front yard, who I didn't know, calling to her for another 2 hours...And she FINALLY attempted to hop down a branch, then another, then another...Until finally she got to the lowest branch on the tree, which was about 5 or 6 feet above my head, and then she froze...So I was exhausted and frustrated and sad and crying, and I just laid down in the grass...And that's when she flew right down to the grass beside me and walked right over onto my chest.
***They have a really difficult time with Descending from trees. They can easily fly upwards or straight-across, no problem, or fly slightly-downwards from one tall tree to a lower one, but they just cannot actually "descend" down from a tree to a person below...So the easiest thing for them to do seems to be hopping down from branch to the branch below them, one single branch at a time...So I found it best if you don't stand out near the perimeter of the tree under the branch that they're standing on, but rather stand right near the trunk of the tree...As soon as I did that she walked down the branch she was on towards the tree-trunk, and that's where all the thicker branches are that basically form a "ladder" for them to hop down branch-to-branch...It took about 2 hours of me first calling to her, then me just pathetically begging for her to come down (I had gotten to the stage of yelling "Please Lita...Please...Please come down to Mama Lita...Mama's tired Lita...PLEEEEAAAASSSSEEEE!"...It was sad..)
I always love a happy ending when it comes to this situation, because so many people who have this happen to them never see their birds ever again. That's typically what happens on-average, they lose their birds forever and never even hear them or get a glimpse of them again (I personally believe it's because they do eventually get very tired, hungry, thirsty, etc. and they finally go to someone, and unfortunately most people who find a parrot outside, especially a tame-parrot, well, they just keep them. They don't even bother to advertise that they've found them anywhere, nor do they go online to check to see if someone has posted them as being lost. They don't care, they either keep them as their own or they sell them because they know they're expensive. It's horrible. We actually see it here on the forum more often than we should, where a new member joins to make a post saying that "They just found a parrot outside in their yard or they walking down the street and a parrot was just standing on the sidewalk or in a yard, and they want to know what size of cage they should buy for their new bird"...
Just as an FYI, I have to say it to make myself feel better, but NEVER, EVER, EVER take your CAG outside without him either being inside of a cage/carrier or on an Aviator-Harness and leash. It doesn't matter if he's clipped or not, clipped-parrots get lost ALL THE TIME because they can fly for miles with the air-currents. At 4 months-old, it's the best time right now, if you're not doing it already, to introduce him to an Aviator-Harness, and start working with him every day to first get him to accept you putting it on him (in-steps, you cannot just put it on him all at once, it typically takes a month or two at the least to get them to accept you putting it on them, no matter how tame they are), and then once he accepts you putting it on him fully, then you have to get him to accept wearing it for a length of time without him chewing on it constantly...But you want to start doing the training ASAP, the younger you start, the easier it is to get them to accept it, and the quicker they will get used to it and accept it. Then you can take him with you wherever you go, but do it safely...
. Where she has been predominately is 5 minute walk from home. 
