Just wondering if its allowed to travel to US territories - like puerto rico, virgin islands, bahamas (for our honeymoon) before advance parole?

Any inputs will be appreciated!

Bahamas is NOT a US territory ... would be a bad idea to go there...

US Nationality Act: Definition of United States includes the Canal Zone and all territory and waters, continental or insular, subject to the jurisdiction of the United States.
So travelling to Puerto Rico or the US Virgin Islands (not the British) should be fine without AP.

Read of someone here on VJ who travelled to the Bahamas and forgot her GC at home, not only did they gave her a hell of a secondary inspection, she also had to pay 500 or 600 Dollars for the processing and for them checking on her status. So be careful were you travel to, they for sure won't let you back in when you pick the Bahamas for your honeymoon.

Yes, do not go to the Bahamas. Puerto Rico and the US Virgin Islands will be fine, but make sure NOT to leave those islands. We just got back from St. Croix in January and we had very little problem. Make sure to take enough identification with you to prove that you:

1) Are married (marriage certificate)
2) Have filed for AOS (receipt notice)
3) Are who you say you are (passport AND United States photo id, if possible)

The IO at customs looked at all of these, including my passport (and I'm the USC) and still asked us a lot of questions. Not to alarm you, but you should be sure to take these pieces of information with you. You are absolutely allowed to travel to Puerto Rico and USVI as long as you travel directly to and from those territories with no side trips.

Thank you very much for the inputs!