Eli is planning to leave Patoh city to start traveling through the various routes to explore first. At the current time he has no real interest in gym battles or the league in general. He has much more interest in seeing the region and it's various pokemon. As such he should be fairly easy to set up interactions with.
Kukka - Mostly Stationary
Kukka is commonly found in Kaia Town and will normally not travel far from it due to caring for baby pokemon and her grandmother and a lack of transport options. She could be found in Datu town but she probably wouldn't venture into the caves.
Monte - Sort of Stationary
Monty, being the Leader of Danali's Gym, will spend much of his time in Danali town. However, it wouldn't be unusual for him to travel for various reasons due to his family being in a position to inform him should someone wish to challenge the Gym.