For the Maratua atoll it's still possible (and quicker) to take a public speedboat directly from Berau jetty in Tanjung Redeb via the Berau River (250,000Rp, three hours). These theoretically leave at 11am daily but check at the harbour or with your Maratua accommodation the day before. Maratua resorts also offer this trip as a more expensive charter.
Bus & Taxi
A handful of buses operate from the oversized Terminal Rinding, on the road to the airport. They include a morning bus to Samarinda (200,000Rp, 15 hours) and a DAMRI bus to Tanjung Selor (50,000Rp, three hours, 9am).
Otherwise transport is largely handled by Kijang (shared taxi) operators, many of whom are unlicensed. Kijang gather in the morning across from the former bus terminal on Jl H Isa I and require a minimum of three passengers (more for bigger vehicles); you can buy multiple seats to leave earlier. They will also pick up around town, so ask at your accommodation or at the airport. Destinations include Tanjung Batu (100,000Rp, three hours), Tanjung Selor (150,000Rp, three hours), Samarinda (400,000Rp, 14 hours) and Balikpapan (500,000Rp, more than 20 hours).
To charter a taxi from the airport to Tanjung Batu costs 500,000Rp.