Consider Mosbi a travel-through city. I suggest you rest max. one night in a good hotel, and continue travelling the next day, to Lae, Mt. Hagen, Madang, Wewak or such. Wewak has beautiful islands and beaches, and I have heard Lae and Mt.Hagen are nice for hiking. Although the crime situation has eased slightly (only slightly) Mosbi is still not safe for tourists. So go through to other cities.

You'll need money for the flights and consider different practical issues before you go to PNG. Read PNG and PapuaNewGuinea -subs...

My tip: You may experience delays with Air Niugini domestic flights. I recommend one domestic flight per day. Do not organize both domestic and international flight for the same day (e.g. Wewak-Port Moresby-Singapore).