This app was mentioned in 12 comments, with an average of 1.92 upvotes
GPS works everywhere, but you'll only get strong data signal on your phone while you're on the east coast. Once you reach the north coast it gets spotty and there's almost no signal around the west coast or further inland. So don't plan to rely on anything that uses an internet connection.
Bring a good map... Or two. Whatever digital maps you want to use, make sure they still work offline. My favourite (which I used for the NC500 last month) is All-in-One Offline Maps for Android, as it's free. Before you leave you'd download the full general overview and closer detail views of the general route and nearby areas you'll be visiting. It lets you zoom in close enough that you can see features like waterways, tracks, car parks and interesting walks. Mapnik and the Hike/Cycle maps are brilliant, both based on OpenStreetMaps. Download an offline view in Google Maps too for in-car navigation if you don't have a standalone GPS.
Tourist information centres sell wee booklets of walks around different parts of the north, highly recommend these. I don't know how you're doing it, but in January, I'm guessing driving from B&B to B&B? The most memorable experiences you'll have will be on foot in wild places. The walk booklets contain walks for all levels of fitness. Just make sure your footwear is waterproof and you bring a spare set...
Stop and explore anywhere that looks interesting, not just the tourist traps. The OSM map I linked shows paths and tracks so you can explore along your route and get an idea of where there may be good walks which aren't signposted on the road.
The main big supermarkets are a mega-Tesco in Wick in the north-east coast, a Tesco & Lidl in Thurso on the north coast, and a Tesco in Ullapool on the west coast. I don't do restaurants or pubs but there were no shortage of those, just some odd opening hours.
all in one offline maps (for android) It's a comprehensive map app that lets you download as much as you have space for. Highly recommended
https://play.google.com/store/apps/details?id=net.psyberia.offlinemaps Free usgs topos and many other maps to download gps enabled. http://www.mobilemaplets.com This one's the shit. You can download maps people have made or georeference your own geologic maps and download them for offline use. Also free. I've uploaded quite a few geologic maps around Colorado and Wyoming (including the 1:500000 state wide maps from the '90s)
The interface can take some getting used to. You can download maps from many different sources including trail and topo. Only limit is free memory.
I've come to absolutely love Psyberia's Offline Maps. You can do anything your map fetishes could desire. Custom maps, layering, editing, waypoints and much more. Even great for sharing POI with people or recreational activities. Other than that Google Maps will suffice for most things.
Printed out maps will turn to shit after about a minute in even pretty mild rain, unless you laminate them. They're also a nightmare to stitch together to route plan over much difference, especially if you're in a hurry. I'm sure you can find some more resilient ones for sale.
Additionally, there are good apps where you can pre-load topo maps so you don't need to internet connection to use them - just GPS (or just use them like a regular map without GPS. I use All-In-One maps but I'm sure there are a ton of options out there. It's fiddly to figure out how to download and store maps for offline use, but you get used to it after a bit of playing.
All in one offline maps. You can choose different maps to load in it, including Google maps and Google satellite. You can download some of them for offline use, but not the Google ones thought. https://play.google.com/store/apps/details?id=net.psyberia.offlinemaps
Even if you did want offline satellite maps, it would take up a lot amount of space.
You could try this.
All In One Offline maps. Numerous maps to choose from and you can even overlay them
I like this one a lot. https://play.google.com/store/apps/details?id=net.psyberia.offlinemaps