There's quite a lot of plains and forest between them and Khazad-dûm by the straightest path. Notably, the dwarven city-nation seems to be due south of the triple peaks Ellisaria and Brisingr cleared of orcs earlier.
Their flight takes them over the southern expanse of the massive forest Thorin's map identified as 'Mirkwood'. It has a foul sense to it, unlike the dark, brooding, but mostly wild taste of the northern reaches. Thick spiderwebs throng some of the trees, and a ruined fortress sits upon one lowly hill - it seems to have been blasted apart rather recently, and the sunlight seems reluctant to actually shine on it.
Beyond: the vale of the river Anduin, and a tributary that passes up through an insignificant bit of woods to the lake Mirrormere, by which a cracked but still strong pillar stands. The Eastern Gate, its great stone doors shattered, overlooks the perfectly still waters of the clear lake. The mountains soar up quite sharply from the dale, passing into the clouds above.