Clark, recently mentioined good tips for saving money on grocery bills; including shopping around different stores
Are there any apps or other ways to compare local grocery prices (regular and sale offers) to help maxiimize savings
I have a limited number of grocery stores near me. I also am a COSTCO member.
Comparing prices store to store on particular items is difficult for me. I know from experience certain products will be cheaper at a particular store, however traveling store to store is not cost effective. I do look for sales and closeouts. I buy frozen dinners based upon unit pricing (cost/oz). When shopping for soda I usually get the store brand (Safeway, Walmart) but have seen some sales where the name brand was almost the same price on sale and I stock up.
I but lactose-free milk at Costco. That means I have to get 3 at a time. I free two and pull one out of the freezer into the fridge a few days before I will be using it. I get it at Costco because the local supermarket is so much more expensive that I can throw some of the saved milk out and still save money.
Even buying meat on sale or in a large quantity at Costco, I can still save money by getting it elsewhere. I helped start a pet food co-op. We buy meat from the local producer. It is USDA inspected, local, grass-fed beef and the same meat is delivered to the local supermarkets (Costco gets theirs from the mainland). Because we are getting it direct, we know what the supermarket markup is. I can buy just a pound or two of ribeye steaks and pay a few dollars less a pound that Costco and not have to buy half a cow! The co-op can offer the pet owners meat for their animals that was originally going to the dump, so it is a win for all of us.
I do not necessarily buy dented can food because due to prices here,they tend to be all gone pretty quickly. ALso, visitors to our tourist area are put off by high prices and grab the cheaper stuff too. Since many visitors arrive on a Saturday (condo and timeshare people), better shopping deals may be Thursday night before the Friday-people-getting-paid horde hit the stores 
Our Safeway has a $5 Friday and I have been known to arrange a shopping trip (20 miles each way) to get those deals along with other items. They sometimes have an 8 piece dark meat chicken selection at the Deli counter (limit 2) and I will get two of them. It is not the greatest fried chicken I have ever had, but its is great for the money. Those 16 pieces would cost just over $10 but around the corner at KFC, I would get a slightly better selection (chicken bucket includes 4 drums, 4 thighs, 4 breasts and 4 wings) for $50. So 1/5th the price at Safeway? SOLD!
Compare prices in sale fliers or on the websites. Buy items on sale and stock up. I am not against going multiple times in a couple of days to take advantage of a limited number of items available. Also, if there is a limit of a few per person, I have family members check out themselves also with the limit.
We have quite a few grocery stores nearby. I usually shop at Safeway, Sprouts or Trader Joe’s. On rare occasions at Bashas. Depending on my main planned purchases as to which store I’ll head to. Sprouts has good produce and produce prices; ditto with meat. Trader Joe’s has good cheese and cheese prices, good cookies and their prices, good snacks and their prices, good wine and beer prices. Safeway has a wider variety of products, good sales, and mostly decent prices. Household goods are more expensive than target or Walmart, but Safeway is more convenient. A few years back, Basha’s did a major remodel, and completely closed for many months. I used to shop there frequently. Now only rarely. All because of a mostly unnecessary remodel. I doubt I’m the only regular that they lost.
Kroger usually mails me coupons of things I regularly buy, such as a free Almond milk, so I will use those first.
Then to Costco for the bulk items and any groceries that aren’t too large to use up. Oh, and a hotdog on the way out!! 
Trader Joes has great quick meals for one or two and is priced right.
Lucky for me, Kroger, Trader Joe’s and Costco are all near each other.
Publix is the closest to me, so I pop in if I need something quick, but they are usually pricier, unless they have one of their BOGO specials of what I usually buy.
Key is to not buy anything just because it is on sale or you have a coupon, buy only what you need!
I think this was a question that appeared on the 2/22/24 podcast, and it appeared as I was typing a post about it.
Flipp is an app that allows you to search a myriad of stores for items that are on sale as well as view store circulars.
You can also use coupon blogs. I’m in the Southeast, so SouthernSavers is my main resource. She covers a lot of stores common in the region like Publix, Kroger, Lowe’s Foods, Winn-Dixie and of course the national drug and big box stores. If you web search “[store name] coupon blog,” you may be able to find a blogger who covers the same of that store and/or a mix of stores in your region.