I think there should be a Trainer Tip reminding players that they can check their /pokegear for the next gym location. I just realize that its a common question like "Where's the first gym" "Where do I go next" and so on.
I agree with your trainer tip suggestion because the other options are searching for a gym guide in forums and word of mouth. Obviously if you ask and someone tells you within 5 seconds of your question, its the most optimal solution to finding a gym. Trainer tips would be useful here however trainer tips in pokefind cycle through the 20 - 30 tips every so often. The odds of receiving the 1 trainer tip for the exact situation your in at the exact moment you need it, are very slim. On top of that, some players like me pay no mind to the trainer tips that cycle through chat in-game. For this suggestion to work, we would need a trainer handbook with all the trainer tips incorporated into the item. This way we could read them all at will. At that point this suggestion would function faster than the forum guide we have now but still slower than word of mouth. P.S.i would think when you first get pokegear, the first instinct would be to open it and see its functions and services.