Update Getting iterateable neighbours is pretty easy when you introduce a NullObject for nonexisting cells. (This is also helpful at other places.)

public class Grid
{
    //...
    protected Cell getCell(int x, int y) {
        if (x < 1 || x > getWidth())
            return Cell.NULL;
        if (y < 1 || y > getHeight())
            return Cell.NULL;
        return cells[x][y];
    }

    protected boolean placeBomb(int x, int y) {
        if (!getCell(x, y).placeBomb())
            return false;

        for (Cell c : getNeighbours(x, y))
            c.incrementBombCount();
        return true;
    }

    public Set<Cell> getNeighbours(int x, int y) {
            Set<Cell> neighbours = new HashSet<>();
            neighbours.add(getCell(x - 1, y - 1));
            neighbours.add(getCell(x, y - 1));
            neighbours.add(getCell(x + 1, y - 1));
            neighbours.add(getCell(x - 1, y));
            neighbours.add(getCell(x + 1, y));
            neighbours.add(getCell(x - 1, y + 1));
            neighbours.add(getCell(x, y + 1));
            neighbours.add(getCell(x + 1, y + 1));
            neighbours.remove(Cell.NULL);
            return neighbours;
    }

}

And the cell class:

public class Cell {

    public static Cell NULL = new NullCell();

    public static class NullCell extends Cell {
        private NullCell() {
            super(null, -1, -1);
        }

        @Override
        public Set<Cell> getNeighbours() {
            return Collections.emptySet();
        }

        @Override
        public boolean placeBomb() {
            return false;
        }
            //...
    }

    private final Grid grid;
    private final int x;
    private final int y;
    private VisualState state = VisualState.HIDDEN;
    private boolean bomb = false;
    private int bombCount = 0;

    public Cell(Grid grid, int x, int y) {
        this.grid = grid;
        this.x = x;
        this.y = y;
    }

    public Set<Cell> getNeighbours() {
        return grid.getNeighbours(x, y);
    }

    //...
}