What exactly are you looking for?

NJ isnt a Bon Jovi museum. There is no Graceland here. The 2 places I could recommend is Asbury Park (but even more so The Stone Poney) and the Soul Kitchen in Red Bank.

Asbury Park caters more towards Bruce but there's still a lot of Bon Jovi memorabilia around and afterwards you could go to the Soul Kitchen for a good cause.