Taking a bike seems to be a convenient choice if you stay for a while here in Balikpapan. You may come and see this web site to have a look at the motors choice. I recommend it to you. The guy in the site says that he usualy rent it to some young French expatriat. You might be interested in it. Check it out..www.rentalbagus.com
One thing I really like about Balikpapan is that it's easy to get around. And the few days I was there, I did not feel that I was cheated on the fare because I'm not local; there are slight variation on the fare each time I got into the 'angkot' but it's quite negligible. Oh, as far as I know (and being first time short visit there), there are two public transportation choices there - taxi and 'angkot'; taxi being more expensive (I don't know by how much since I mostly use 'angkot' due to its convenience). The angkot is color coded so you could ask around which angkot to use for your destination; but I think Balikpapan is not that big so it's not difficult to get around.
In my case, transfer from airport to hotel was arranged but just in case, there's main road just outside the airport and you could take your 'angkot' there. As you exit the airport, city center is to your left, I think about 8 ~ 10 km from airport. I believe this is a cheaper option compare to taxi; the fare for 'angkot' should not be more than U$2.00. As you can see in the photo, main road is near the airport and the green 'angkot' plys this route.