Food 4 Less is west on Katella in a shopping center with a Sav-On, Taco Bell, Burger King, Arby's, Baskin Robbins, and the aforementioned Hometown Buffet. FFL is a no-frills bag-yourself grocery store that is the low budget entry in the Ralphs grocery chain. That being said, it's where we usually shop because the prices are lower.
Albertson's is another grocery store chain that has a few locations in the area. I believe there is one south of DL on Harbor, but the two I'm familiar with are further west from FFL on Katella at Brookhurst and then even further on Katella at Beach Blvd. This last one is especially large and nicer and is combined with a Sav-On and a decent deli section and a small food court. But it's more distant, probably about 5 miles west of DL.
To answer the original poster, FFL is the only grocery store that I'd say was in walking distance, but it's a healthy walk, probably 30-45 minutes from the DL Hotel. There is a liquor store at Katella and Walnut, due south of the DL Hotel, but I'm not sure what they carry besides the obvious. That store is not too far out of the way to the 7-11 at Harbor and Katella, so might be worth checking out.