Once you have obtained the water and air cores in The Legend of Legacy, you will most likely be stuck since new maps may not be available at the time to explore (either you have unlocked it by exploring or purchased it through the merchant in Initium).
To progress after obtaining both of these cores, you must go back to the ‘Deserted Village’ map.
Once you have entered the map, go down the steps and go straight to the top-right corner of the village. The option to travel should appear on the bottom-right corner of the 3DS’s top screen. Press the “A” button on your 3DS to go to the next location (Monument Hill).
After obtaining the air and water cores, you need the fire core before going to the Deserted Village map. The fire core is located in the Valley Ruins map. You can find it by discovering an exit somewhere in the Roaring Valley map (most likely the Bagpipe Ravine in Roaring Valley).
You can unlock the Deserted Village map by looking at the top view in the Scenic Ridge of the Roaring Valley map.
You should find three stones. Go to the last one and press the A button. If no new events take place after, sleep in the Inn and you should find something new to be done.