Rembang is a working town on the north coast of Central Java, east of Semarang and west of Tuban. It is not polished, but it has a useful place on a slow Pantura route: Kartini history in the town centre, Java Sea beaches just east of town, and Lasem's old Chinese-Javanese quarter close enough for the same day.
The strongest stop in Rembang itself is the R.A. Kartini Museum, housed in the former regent's residence where Kartini lived after her marriage. It gives the town a clearer identity than many ordinary north-coast stops, especially if you already know her letters and her role in Indonesian education and women's rights.
East of town, Karangjahe Beach is a local picnic beach with casuarina shade, snacks, and calm water rather than a wild coast. Continue to Rumah Merah Lasem and the surrounding streets if you want the more atmospheric side of the regency: old Peranakan houses, batik, temples, and a long memory of Chinese settlement on Java's north shore.
Rembang rewards travellers already crossing north-coast Java. It is less convincing as a stand-alone detour, but as a one-day stop between Semarang, Kudus, Lasem, and Tuban it has enough texture to justify the pause.