You don't need to use a bomb to get through the tunnel, the Forest Bandit mob at the "normal" entrance is slow enough to walk around (just have to be a little wary of the timing with the bandits directly below), and the bandit leader is likewise slow enough to lure into the table that's blocked with a chair, which makes getting around him trivial.
As Annogiemouse mentioned, the four "immediately" accessible Star Metals are in the Central Forest, Northern Forest, Bandit Hut, and Refugee Camp. Day 2 (assuming you became an adventurer, anyway) gives you access to the Northern Mine, and after starting Spider Cleanup you can get the Star Metal there.