Andrew - how is it my smart phone doesn't need service to work -- do you mean it will work just like it does here in the States using the local provider? Vodafone or some such?
To work as a GPS, you phone doesn't need actual mobile service. The phone will pick up a GPS signal in the same places a "regular" GPS will - in the mountains, anywhere it can communicate with satellites. Occasionally, like a "regular" GPS, it will lose reception when blocked by tall trees or something.
But to see your location on a map and get directions, you need to download the local maps ahead of time. Google Maps for example has an "offline" mode - go into settings and find the "offline area" and download the part of western Slovenia and Trieste where you'll be driving. The larger the area of map you choose, the more storage space it takes on the phone. Maps are good for 30 days then must be renewed.
You can try Google Maps "offline" at home. Download the map for the area where you live, then put the phone in airplane mode and try navigating somewhere. The "offline" mode works only for driving directions - not for walking/public transit directions.
Of course, without mobile service, your phone won't get calls, texts, or any internet service unless on WiFi.
Your US phone may have an international roaming plan. Sprint and T-Mobile both offer free unlimited data overseas (but limited to 2G speeds). Verizon and AT&T both charge $10/day for days you use the phone (or you may be able to buy a monthly plan with limited data and calls). None of them has actual service there - they have roaming partners. If your phone is unlocked, you can buy a SIM card for it in Slovenia. It's still nice to have data on your phone. Google Maps "offline" doesn't have traffic info - you need data for that.
