Before I got a stand-alone GPS unit (then smartphone after that), I used OffMaps that stores maps for offline use. Paid for some of the maps (like DC area). I managed to get around fine, but it did come in handy. I don't know if they still map offline maps given how more people than ever should be on internet enabled phones, but worth a shot. Worst comes to worst, there should be a way to download maps from map services like Google Maps or Apple Maps.
Everything else... just check the app to see how it runs offline (if at home, turn off wifi). Some only requires you to be on wifi to download the app initially, updates, files, etc. (although if you're old school, you can still transfer stuff from your desktop computer that DL's the stuff via Ethernet). Others may have some features that require internet access. In extreme cases, you'll have limited use or no use without internet.