Not sure what is your preference for shopping but if you are inclined toward western style shopping malls, the newest, flashiest (and probably the largest) is situated on Le Loi boulevard, the whole block between Pasteur St and Nam Ky Khoi Nghia St, and anchored by the Takashimaya store. It opened on Feb 2016. BTW, don't get turn off by the appearance of Le Loi Blvd as a big construction site, as an underground subway station linking the Ben Thanh market and the Opera House is being built.
Or you can visit the Crescent Mall in the high end residential area of District 7.
For restaurants, if you have not yet tried the favorite "banh xeo" (vietnamese crepe filled with pork, shrimp, egg, bean sprout, onion), you should go ask your hotel staff to write down "Banh Xeo Dinh Cong Trang", the restaurant is located on Dinh Cong Trang street, off Hai Ba Trung street, near the Tan Dinh market. This is a simple eatery, with plastic chairs and aluminum tables.
Next up, you can stroll to the narrow and short Ngo Van Nam street (about 5 min walk, north from your hotel) where you can dind many restaurants. A good vietnamese restaurant there is the Quan Bui.
Take a walk along the Nguyen Hue pedestrian boulevard from the Saigon river down to the City Hall. A good place to eat is the Cocochin food court, opposite of the Palace Hotel. Several well know Saigon eateries can be found there. You will receive a plastic credit card type upon entry and your order will be charged on that card (pick an appetizer, a main course, a dessert, a drink from different eateries if you wish) and you settle the bill when showing the card upon exit.