Even though we cancelled our phone services with Verizon and AT&T, Auston and I both wanted to bring our iPhones with us while we traveled. I assumed it would be to listen to music, snap a picture if our regular camera wasn't handy, or to go online while connected to wi-fi.
I did not expect to find so much more use out of them though. I was very pleased to find that the GPS function on the iPhone still works without cellular data and without wi-fi. This means you can use it for free. A phone service connection and/or wi-fi would help the GPS location to be a little quicker, but it is not necessary to be connected to any service or wi-fi.
This is when I found an awesome iPhone app called OffMaps 2. For $0.99, you can buy a map of the city you're in and OffMaps 2 will show you where on the map you are located. The problem with Google Maps is that it does need to be connected to wi-fi or a phone service to load the map. But OffMaps preloads the map and saves it to your phone. (You must be connected to wi-fi or cellular data to get the app and a map of course.)
Anyway, we purchased the map for Mexico City and it has been extremely helpful in getting us around. It even has the train lines on the map. It's definitely traveling in the 21st century and I'm ok with that. We'll see how the other cities we visit work out.
Note: This app could also be used when traveling in the US if you don't have unlimited data and you need to save the total usage. I believe there are also similar apps to this one. So you don't have to go with OffMaps 2
This of course means that the Compass app will also work on your phone with GPS only.
The next app I've found helpful is XE Currency. This will give you the most current exchange rate between multiple currencies. You have to have service or be connected to wi-fi when first choosing which currencies you want to convert between. But after that, the app works independently of any type of connection.