Having relatives in that exact area...$200/week is realistic, depending on how you eat. If you like meats (especially lunch meats)/non-seasonal produce/single-serve packages/organic/name brands/pre-prepped items, etc...you're gonna spend $200/week or more where you live.
Echoing advice above, I also encourage you to walk through a local grocery store and look at the prices and the ads and get a feel for what you'd spend. You can likely spend less, but then at what cost to you (a change in diet, a commitment to only eating the seasonal/on-sale produce, a desire to drop high-end coffee or soda, etc, etc, etc)...
It's also affected by your storage ability. If you have no way to store meats (for example), you will either have to always eat the on-sale meat for the week or you will have to play the flucuating price to eat what you want (chicken breasts can be between $2-$5/lb, ground beef can be between $3.49 and $7/lb, depending if it's on sale or not)...