I'm using Mapzen right now, and it's really solid, but I'm not sure how well it'll scale.
I didn't know about Mapzen. I'll check it out. I've looked at Mapbox myself. It's free up to a certain amount of connections per month (not a whole lot of connections though, and the prices increase pretty sharply if you need more than the basic amount of connections).
Eventually, if the game starts taking off, I will get some servers. You're definitely right about the multiplayer tho, and the cheating is definetly a big concern, but I'm hoping there's a way to combat this without reporting everything to the server.
I'm not going to say this is impossible, because nothing is impossible, but it's definitely very difficult. Even reporting everything to the server is not enough -- the server actually has to make the decisions. For instance, if you let each client spawn its own enemies and its own loot, then someone will make a hacked client that spawns level 1 enemies with level 100 loot. It's a lot of trouble to make a hacked client, though, and people will only do this if the game becomes really popular, but I feel that we should plan for success.
Strategy and rougelike were my first ideas, but I can't see how to make these work with GPS. I feel like I'm missing something obvious.
You could make a basic roguelike-like just copying the exact formula from Pokemon Go. Instead of catching monsters you fight enemies and collect loot. Instead of getting better and better pokeballs, you get better and better weapons, spells and armor. You can have ranged and melee weapons (if you have a ranged weapon, you can attack an enemy from afar, if you have a melee weapon, you have to walk up close to the enemy). Instead of pokestops and gyms, your map can contain taverns and merchants. I'm kind of tempted to try and make something like this, if I can find the time and energy.
I'm in Canada, trust me I have winter in mind
I'm thinking some audio-based gameplay could help combat this (eg. take your pokemon for a walk, your phone is closed and all input is through earphones).
Another thing that could work for playing in winter, would be if you could actually do a lot of things from your house. For instance, if you made a strategy game that required collecting resources, you could have the player place outposts, coal mines, lumbermills, farms, etc. around the map, and then subsequently control his empire from his living room. You could maybe have certain buildings (forward HQs) that would let the player interact with the map around it as if he was physically there.