GPS does not necessarily use data, you just have to carefully examine the apps that are going to use the GPS and determine what they are going to do with that data. For instance, Google Maps will use the GPS data to determine what maps to download. It's the maps that eat up the data more than the GPS. So look for apps that cache data and/or have "wifi only" options on when they upload. You can still use and save GPS data without affecting you data plan as long as the app doesn't need to be in communication with the web to work. You may even be able to turn off cellular data to see if the app will function properly without internet access. I have been able to download maps to my iPad and use the GPS for mapping, and save my routes, even when my data was turned off or I was in a dead zone. I imagine the same thing can be done on Android. I just haven't needed to do that yet.

I don't know about Strava. I assume it uploads your route info, and therefore uses your data plan, but I don't know how much data it uploads. And it might be able to save the relevant data to upload later, but it does seem like there's info online that Strava also will want to have access to.