Hi,
My suggestion would be Manny's Grille. My family and I have eaten there for years and they have a HUGE selection. All of their food is made to order and I don't think we've had one complaint since we started frequenting them. They do deliver all over the West Ashley area and are open for lunch and dinner. They have everything from appetizers, sandwiches, greek food (which is the specialty), steaks, burgers and the list goes on. Reasonable prices for good food.
They also have a current coupon to use. It is for $10 off a $25 order. When you click on the link, the coupon banner will be at the bottom of the page. Their menu and contact information is also on the website.
Manny's Neighborhood Grille-Charleston, SC::.. Authentic Greek Food like Gyro's, Greek Lamb Shank, Greek Chicken, Plus Pizza, Wings, and Lunch Specials With Your Own Private Television
West Ashley also has all the major pizza chains: Papa Johns, Dominos, Pizza Hut.
It's been a few years since I've lived in West Ashley. I'm now about 20 miles away, so delivery isn't something we frequent from there. (although we do make our share of drives over the bridge for Manny's, lol)
It is such a large area, I'm sure there have been new places opened up that will deliver. Perhaps some others will have different suggestions. Good luck with everything and Happy Health to your parents