Changing grocery store for credit card rewards

So I am 25 and have solid credit for my age. I just need to add more credit history and the one account I used before to build my credit is really not worth it any more. Im looking to get a credit card and focus on cash back. Many have solid rates at grocery stores but the store i go to does not accept credit. I have considered changing where i shop, but this place is by far the best in terms of selection and price. So long as i don't get to caught up in my choices, i spend very little. There are other options around me but to get the price and selection i get now, i would basically have to go to 3-4 different stores to spend the same amount. Would anyone else think it would be worth it to shop somewhere a little more expensive to get the cash back? If not, what other types of cards would be good to look at?