A few things you might want to add to the OP for people who are just getting into the game.
To find potential Pokestops/Gyms near your house you can use the map from Niantic's other game, Ingress, at ingress.com/intel. Each "portal" is most likely a Gym or a Pokestop. You will need to sign up for Ingress, but that doesn't take much, can always remove the app after you get logged in.
To see exactly what natural spawns are around you and what the remaining timer on them is you can use pokevision.com. It doesn't work to show Lured or Incensed Pokemon, but it gives exact locations using Niantic's API. With the tracker broken, this is the best way to find what is nearby. You can also use it to scout other locations.
Lastly, this map: https://www.google.com/maps/d/viewer?mid=1anyDs-H7hOtGQaxaTwuLjulUrVM shows where reported Pokemon Nests are. Great to use to find those rare guys you wanna try to level up. It is crowdsourced, so there is potential that some of the data is false. However, you can use pokevision.com to confirm before heading out!
