Batteries and razors were always the go-tos for me for a first time
Go see for yourself !
Not to be snarky…just to point out that in most if not every state they are required to let you in and sell you alcohol. You can scout it out as much as you want before you pick a day to rent that u-haul. 
Toilet paper and paper towels are two things I always get from Sams. That and a dozen excellent avocados.
Be sure to check their “scratch and dent meat” – stuff getting close to its sell-by date. It’s perfectly fine stuff (not like Food Lion’s recycled/repackaged stuff in days gone by) and if you plan on using it fast or freezing it, you can save some bucks. We got 5 pounds of dietary lean ground beef for a silly low price, got home and cooked it all up loose, and froze it. Now if we want some for spaghetti sauce, tacos or whatever its there and all ready to go.
Here in Minnesota, the liquor store is physically separated from the main store, and you have to have a card to get into the main store. However, I’d assume they’d let you in to take a look around if you asked nicely. Or, they have a stack of those “one day passes” printed out and ready to use. Heck, you’re probably going to buy something…
I found the dried yeast a Smart and Final - maybe 1 pound pack? Don’'t recall the price.
We don’t have a Sam’s OR Costco near us anymore…grumble…but just piling on from memory, any paper/disposable products were good (foil, plastic wrap, paper plates, tp…) Bar towels or random pots/pans, if you need them. Jeans. (maybe that was costco) Dairy products, certainly. Tea/coffee, if you aren’t picky. Stationery/pens. Vitamins/soap. Definitely the yeast and other baking supplies, also rice and other generic staples. Seasonal items. Wander around, 2 hours will do it.
I have been told Amazon Prime’s Pantry is pretty darn good and I can say categorically that their shipping center staff are among the brightest and most dedicated workers in America ------- if not the world. 
Note with a one day pass the OP is paying 10% more than the normal prices. Strange as it may seem some of us can’t remember the usual prices for many of the products we currently use. Thus a strategy of the OP simply wandering around could easily result in him making several buys which are worse than at his usual Walmart/Target, etc.
There’s an app for that. Sam’s Club has an app that you can scan the UPC barcode of any product before you go shopping, and it will tell you the price at Sam’s.
Just do like my Dad did. It sure worked for him …
Mustard was on sale. So he bought, no exaggeration, 6 one-gallon jars of mustard.
When he died a few years later he still had 5 sealed jars and one jar 80% full with some mold in spots. Stocking up stuff on sale sure saved *him *a bundle of money.
So I printed out the pass from their website and headed out to the Land of Big Food. I had forgotten an important part of the Sam’s Club experience: their unbridled contempt for people.
I walked up to the lady at the Customer Service desk (which should be renamed the Needlessly Complicated and Unnecessary Paperwork Desk) and handed her the coupon I had printed out from their website. She checked out a few things and pointed out that the registration number from the bottom of the pass hadn’t gotten printed, and that I should go home, get the number, write down on the coupon, and bring it back. My first thought was “You know, I’m actually not trying to pull a fast one here… it’s your website. You should have a stack of these ready to go.” My second thought was “Not only that, but I’m trying to give you money, more money than you would get from your customers…”
On my way out, I passed something I had forgotten about… the Highlighter Ladies. I don’t know what their reason is any more, but back in the day (5-10 years ago) they had a sign prominently displayed by the exits saying that the ladies were there, checking everybody’s receipts against the contents of their carts and doodling on their receipts, as a measure to fight shoplifting. How stupid do they think people had to be in order to put that in place? In order for them to catch somebody shoplifting, that person would have to (a) hide something on their person, (b) go through the checkout line without it being spotted, and © in the 50 feet between the cash register and the exit, take the shoplifted item out of their pocket and drop it in the cart when they know it’s going to get checked.
And the person would have to comply with the requirement that they stop for inspection. If you just walk past, they can’t do anything. “But we wanted to highlight his receipt and he said no” isn’t a valid defense to a charge of unlawful imprisonment, AFAIK.
It varies from store to store. at the Cicero ave. store in Chicago I was treated with hostility for even asking about the one day pass, but at the store I eventually decided to go to they could not have been more nice.