fairsharefoods.com/do/viewAd
Local mom and pop grocery store weekly ad. You can buy pigs' ears and tripe and all sorts of other goodies here. Also nice jars of pesto, assorted Greek olives, etc. They make their own Mexican chorizo.
Meats, fruit and veg are mostly priced per lb.
Their fresh fruit and veg are always nice and reasonably priced compared to other places.
www.ultra-foods.com/weekly-ad/forest-park/
Another weekly ad here. This place is a local chain.
www.allweeklyads.com/tonys-finer-foods-weekly-ad/
More here.
They carry a large European, Middle Eastern and Asian selection in this particular store. I get greek style yogurt with a middle eastern brand for $2.99 for a really big tub. They have Polish ribena-style drink, jams, chocolatebig sacks of basmati, jasmine and all sorts of other rice from Pakistan and India and occasionally Japan, huge Mexican selection (dried chilis, etc)
weeklyads.aldi.us/Aldi/BrowseByPage/Index/?StoreID=2624213&PromotionCode=Aldi-161102INSc&PromotionViewMode=1
Aldi. Meat here is poor quality imo, but other items are good value and decent quality - flour, sugar, cocoa, canned pumpkin (half the price it is elsewhere but they only stock it for Thanksgiving), tortillas, canned tomatoes and beans, frozen veg...
I find Target a good deal more expensive than other places and I only buy catfood in Whole Foods.. Some individual local stores that are part of chains tend to be more expensive than others.
You will always find some place with milk or eggs on sale, and bread too. Items like breakfast cereals are cheapest in Walmart unless there is a sale elsewhere. I can get my favourite Tetley teabags in Walmart and nowhere else.
Getting the cheapest deal on what you need or will use involves a good deal of driving around, maybe a few trips to different shops every week. If you're prepared to do that and suck up the price of petrol and the hassle of traffic you can do ok, price wise. However, I still think UK and even Irish prices are better and the quality of some items in the British Isles is infinitely superior - meats have a taste, mushrooms ditto, and other veg too, especially if locally grown.
(OP, to find a Target with fresh food, you have to look for a SuperTarget.)