"Any suggestions are welcome !! will just find couple of things to do near Palace before my i can go in at 2:45 pm."
I am thinking you will not have all that much extra time. Westminster Abbey takes 2-2.5 hours, so if you are in at 9:30 you'll be out at 1200. You'll walk to find some place to eat, spend time eating then walk to the visitor's entrance at Buckingham Palace.
You ~might~ have time to:
-walk thru St James's Park
-Stop in at the Guard's Museum on Birdcage Walk.
-Loop around behind Westminster Abbey and see the Jewel Tower
-If you think you will have a lot of time, go to the Royal Mews (the stable for the Queen's horses and the royal carriages). There is a combo ticket for the State Rooms and the Mews. Personally, I don't think you'll have time for this.
Do download the Westminster Abbey app before you travel and tuck your earbuds in your purse. It's much easier to listen to it on your phone than carry around the big audioguide. Both are free.
Places to eat:
-The Laughing Halibut as mentioned before and I ~think~ there are some other eateries around there.
-Pret a Manger - there is one near Westminster Abbey down Broadway. https://goo.gl/maps/anyPy1dvbMJcDVYz5
-I've seen some mention the restaurant at the Methodist Central Hall across from where you'll exit Westminster Abbey but I've never eaten there
-Down closer to Victoria Station there are a couple of new mall/office buildings with a number of eating places. There is a Zizzi's that's pretty fast.
-There are a number of pubs in the area as well - I'm not much on pubs so maybe someone else can steer you there!