1. Gyoum Super. 業務スーパー
This is one of the cheapest places to buy bulk goods. It has good prices and a a lot of choice. However if you're looking for healthy, organic foods they are harder to find. They also have a good selection of alcohol.
2. Okuwa オークワ
Your standard supermarket. It has a decient selection of food and goods. Some of them have extra restaurants as part of the supermarket. In addition there are a few of them open 24hours so you can go shopping late at night.
3. Coop コープ
A good selection of organic and home grown foods the selection at Coop is healthy, if a little more expensive than other stores. They have good choices and their meat is reasonably priced.
4. Kinsho
Another good store with a healthy selection of organic goods. Slightly more expensive than some but if you look carefully you can find some good deals.
5. Sun Plaza スーパーマーケットサンプラザ
One of the cheaper supermarkets it has a good selection of fish and other goods. While the selection is not the best it has some good deals if your willing to look and it's usually in a convenient place. In Nara it has a smaller presence but it's growing.
6. Yamato
Another small supermarket located only in a few places it is in the middle range. However it offers a 10% discount on everything every Thursday. It's meat is very good and if you search around you can find something here for the budget shopper. It also offers special deals such as 40% off meat but only every second month on the second Monday of that month.
7. Seijyo Ishi
If you want expensive imported foods then this is the best place to go. You can find regular goods cheaper in other stores but sometimes if you need a reminder of home this is the place to go.
Those are just a few of the supermarkets around the area. There are many more smaller ones but strictly speaking the best thing you can do is travel to as many as you can find and comparison shop. I didn't mention the myriad of other local supermarkets that I've only been in once either because they are too far away or too expensive.
Good luck and I hope you find what you're looking for.