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If you don't have an iPhone you can buy spare batteries as well as carrying charger blocks.
You have a smart phone with batteries you can replace? Which is it? I have an old style phone with no internet connection, hence the long battery life. It means I can go camping for a week and still stay in contact if needed.
Yes, downloaded offline maps would be ideal. I enjoy the process of navigation / orientation, and find satnav irritating. I think however I'd like to stop carrying paper maps around.
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Most non iPhones have replaceable batteries, I personally have a Wileyfox Spark X (£120 RRP)
For your budget you could buy a budget/second hand smart phone, a charger block and get a sim card only plan for a month at a time when you are touring. You could probably even get a tablet if you'd like a bigger screen.All you need to consider is battery life, screen size and cost of replacement batteries.
Edit: Not sure any tablets have replaceable batteries.
I had similar requirements and was never impressed with the cost involved in buying a cycle computer.
I've ended up using my phone.
There are lots of map apps and navigation apps that work really well and as you said your phone lasts for days compared. If you don't have an iPhone you can buy spare batteries as well as carrying charger blocks.
You can use offline maps so you don't even need an internet connection. Just the GPS on your phone is required.