Since the game level is a board and people move on squares in a grid, you could find the square you want to move to, mark that sqaure as 0. Then go outawards in a circle pattern so the next squares surrounding that would all be 1, then go outwards again and all those squares would be 2 etc until each square on the board is covered. Dont count squares with a wall as you cant move there. Now all the person who is moving needs to do is to always move each step towards the sqaure with the lower value to the square its currently standing on to move there.
You could artifically inflate the value of squares under certain conditions to make those squares less attractive to move to, such as if an enemy drops a bomb then that would add say 100 to the sqaures value and would radiate 99, 98, etc for the bombs explosion range. The person would avoid those squares and find a path around them.