As you exit the hotel grounds, turn RIGHT and go about 4 blocks down. There will be a large pedestrian bridge. You have to climb stairs, cross the street, and descend. There is a Tesco Lotus on the other side of that bridge, and I would best describe it like Walmart or Target. There are groceries, clothes, just about anything you could need. It might pay to take a taxi back to the hotel if you buy a lot in one trip, depending on your cash situation. To/from Tesco was about 45 Baht each way (call it $1.50 or so) and we'd always round up to 60 or 70 Baht as tip to the driver.
The restaurant at the Bangkok Rama has excellent food and is inexpensive compared to some restaurants out around town. I ate more than my share of chef's salads, or the fried pork and spaghetti with marinara sauce.

There is a Seven Eleven just about 1 block to the right as you leave the hotel grounds too, for quicker access for minor items.
The hotel grounds are large and you may walk a long way to reach the front. Best that you be as prepared as possible before surgery, because afterwards you will want to minimize walking and will be tired a lot.
Good luck! I'm leaving for home tonight and have been completely satisfied thus far with my surgery and results from Dr. Chettawut.