I checked my original PDF after adding a comment in Adobe Acrobat Reader and it did not had the comments. I opened the PDF through RECENT in the app and the comments were there! So where are they actually syncing. I finally uploaded it to my Document Cloud to sync but there must be a local storage location? If not can I sync my Documents locally?
I would assume Acrobat reader stores them in the app-private directory. The documents are there saved securely so that other apps can't access them. Unfortunately this also applies to the the user, so that you can't access the file on a non-rooted device.
If your device is rooted you can check the directory
/data/data/com.adobe.reader which is the app-private directory of the Adobe Acrobat reader app.
Also check it's subdirectories. Most likely you will find the saved PDF file there.