When I am planning to do a multi day long distance walk, one of the most important things I look at is where I can find food and water along the walk. If there are many shops along the walk, it might mean that I don't have to carry food and can simply buy food on my arrival for my tea and then breakfast the next morning if I'm staying in a Hostel and then maybe buy a sandwich for the next day before I set off. I find that shops like Co-op's and Spar's are good as they usually open about 07:00 and many are open late night until after 22:00 which is good if you arrive at your destination after most other shops are closed.
If there is not a shop at the end of the day, it could mean having to carry food that day with you (or pack some in your baggage if someone is carrying it for you) or finding somewhere along the days walk to pick up some supplies. You don't want to be carrying any more weight than you need to so there's no point carrying food for 20 miles if you know that there is a shop at the end of the day or along the route.
I have listed below some shops that I found along the Coast to Coast walk West to East when I walked it in May 2014 and September 2014 to help your planning. These shops were open when I wrote this in 2015, hopefully they will all still be open when you do your Coast to Coast walk. Remember that shops may be open later in Summer and sometimes closed earlier in the Winter.
Places to buy food along the trail
St. Bees is the start of the Coast to Coast if you walk West to East and has a shop in the village that is open until about 8pm, where you can pick up a few things for the first couple of days. There's also a few pubs serving food and a chippy to have a last meal before heading off in the morning.
Cleator is on the route and has a small shop in the village as you pass through where you can grab a snack or something to drink before walking up Dent. Cleator Moor is a mile or so off route but has a wider choice of shops but not worth the extra mileage.
Ennerdale Bridge has no shop but has a couple of pubs if you feel like a break and something to eat and drink before heading towards Ennerdale Bridge Youth Hostel.
Honister Slate Mine can be found a few miles from Rossthwaite and has a cafe selling hot snacks, hot and cold drinks and also plenty of cakes to take away or eat in the cafe. A good place to have a rest if you have chosen to walk the high route from Ennerdale Bridge over Red Pike and the ridge to Haystacks.
Rosthwaite seems to have a little Post Office shop although I think it only opens mornings and chances are that you will have left Rosthwaite before it opens or arrive when it has closed for the day. You will pass the doors of Borrowdale Youth Hostel just before the village and you can have something to eat in the cafe which is open to the public or buy a few things from their shop.
Grasmere is a popular tourist spot and has a few shops including Outdoor shops, bakery, cafes and a Co-op which is open from 07:00 until 22:00 every day.
Patterdale has a well stocked shop in the village which is open from 08:30 until 18:00 most days during the Summer but has reduced hours in Winter. A good place for grabbing food to cook at the Youth Hostel if you're staying there or grabbing a hot breakfast sandwich in the morning before heading towards Shap.
Shap has a couple of pubs as well as a nice chip shop if you don't want to cook. There is also a Co-op in the village which is open from 08:00 until 20:00.
Kirkby Stephen will feel like a big City after many days of walking through little villages and you can enjoy it's many pubs, take away and a Spar which is open from 08:00 until 22:30 every day and a small Co-op in the village open 07:00 until 22:00 and a larger Co-op nearer the end of the town which is open 07:00 until 23:00 Mon to Sat and then 10:00 until 16:00 on Sundays. It's important to stock up in Kirkby Stephen as the next main shop is in Reeth which might be two days later depending on where you stay the next night.
Keld has no shop but the Cafe in the village sells snacks to eat in or take away and sells cold and hot drinks and Keld Lodge also serves food during the day.
Reeth might be somewhere you choose to stay the night or Grinton which is a mile or so further on. Reeth is quite a busy little village with a Post Office shop open from 08:30 until 17:30 Mon to Sat and 09:00 to 16:30 on Sundays. There are also pubs, cafes, an outdoor shop and an outdoor market on Fridays.
Richmond is the next stop and the busy town has many shops if you need to stock up on anything, I stopped at the Wetherspoons for some lunch and a break but there are many cafe's and pubs in the town centre. The large Co-op near Wetherspoons is open from 06:00 until 22:00 Mon to Sat and then 10:00 until 16:00 on Sundays.
Brompton On Swale might be where you stay one night and if you do, the Costcutter shop in the village is open until about 18:00 every day. Not much point detouring to here if you're not staying the night here so make sure you've brought food from Richmond when you pass through it.
Dandy Wiske has no shop but the pub is an ideal place to have a rest and a refreshment. It's possible that you might be staying in the village overnight as there's not much alternatives around this section of the Coast to Coast walk.
Ingleby Arncliffe is where you cross the very busy A19 carefully and quickly. At this junction is a petrol station with a good sized shop inside it where you can grab a snack or a drink before heading over the road. The pub in Ingleby Cross not long after you cross the A19 serves food and is a popular place to stay the night.
Osmotherley is slightly off the Coast to Coast path but you might detour there to stay the night at one of the local guest houses or the Youth Hostel at the campsite, which has a small shop in it. Osmotherley has a few pubs, a chip shop and the small village shop is open until about 17:30 most days.
Carlton Bank isn't actually a place, it's actually one of the hills that you walk over but at the foot of it lies the Lord Stone's Cafe which is open from 09:00 every day and closes at 17:00 Mon to Sat and 16:00 on Sundays. You can choose to have a break and something to eat in or outside the cafe or buy a bar of chocolate and a cold drink from the small tourist shop. There was a small snack kiosk there in the summer of 2014 where I had a breakfast roll but it appears to have closed down but the kiosk remains.
Clay Bank is about three miles further on and there is sometimes a snack van in the car park just along the road to the left before you cross it.
The Lion Inn lies in the middle of nowhere but is extremely popular. You might want to have a break and something to eat or drink here before heading on to Glaisdale.
Glaisedale has a small butchers and shop in the village, the shop is open until about 17:30 but I think it closes on Sundays. There is also a tea room and a pub further into the village near the train station which serves meals.
Grosmont will probably be your last stop along the Coast to Coast walk for food and it has a small shop as well as a couple of cafe's in the village beside the steam trains. Good idea to stop here for a break before heading up the steep hill out of the village and walking the last few miles of the Coast to Coast walk.
Hawsker has a couple of caravan parks, the one nearer to the coast having a small shop but it's only open on certain days, it might be open more days in the summer though. It's unlikely though that you will stop here as Robin Hoods Bay is only three miles away but you might want a break before walking triumphantly along the coast to the end of your walk in Robin Hoods Bay.
Robin Hood's Bay is only a small village but as it's on the coast, it's popular with tourists and has a few little cafes. chip shops and pubs nearer the finish plus a larger shop in the centre of the village beside the bus stop. It's a great feeling to sit by the sea with chips or overlooking the bay with a drink and reflect on completing your Coast to Coast walk before your journey home.