Hi Bert
If you are coming by ferry & bike I would suggest then that you do head south to Kuta. There are many cheap comfortable losmen accross from the beach. I would personally recommend Segare Anak. There is a new place just opened called Surfers Inn being new the rooms are bound to be clean & nice.
If you want somewhere with a pool there is Tastura opposite the beach, or set back in the village Kuta Indah (My recommendation for hotel with pool) Or Matahari Inn.
If you look here you will find a more information on the losmen of Kuta, Lombok.
http://groups.msn.com/LombokLovers/kutafacilities.msnw
let me know if there is anything else I can help with.
Mimpi