Hexagonal grid coordinates

There's no reason why you can't use mouse input on a TileMap. You just have to convert the mouse location to grid coordinates with the world_to_map() function. If you want to highlight a hex, you can either switch to a different tile or have another TileMap over it that just does highlighting. If you want to click and drag, you can create a temporary object at the location to follow the mouse.

However, if you just want to place a bunch of hexagonal objects, you could do something like this.

extends Node2D


func _ready() -> void:
	# Map out something.
	var map = {
		Vector2(0, 0):'trees',
	}

	# Fill a bunch in randomly.
	for y in 10:
		for x in 20:
			if randi() % 2 == 0:
				map[Vector2(x, y)] = 'trees'
			else:
				map[Vector2(x, y)] = 'rocks'

	# the actual textures
	var key = {
		'trees':preload('hex_trees.png'),
		'rocks':preload('hex_rocks.png'),
	}

	var off = Vector2(120, 105)
	var foff = Vector2(60, 70)
	var toff = Vector2(-40, -5)

	for y in 10:
		for x in 20:
			var sp := Sprite.new()
			var lb := Label.new()
			add_child(sp)
			sp.add_child(lb)

			var v = Vector2(x, y)

			sp.texture = key[map[v]]
			sp.position = off * v + foff
			lb.rect_position += toff

			if y % 2 != 0:
				sp.position.x += 60

			sp.name = 'hex_%03d_%03d' % [x, y]
			lb.text = sp.name
			lb.modulate = Color.black

Edit: Thanks to Kenny for the art.