Visit Bomana Cemetery if you get a chance. Suprisingly its the cemetery with the most Australians killed in Wars in the World.
Port Moresby is a young city. There's hardly any old colonial buildings to admire. One of the few that's still standing is the Post Office. It's been there since the early 1900's.
Go up to Paga Hill which has many nice houses overlooking the Coral Sea. It also has a fantastic view of Ela Beach. The road is quite steep and narrow. Be careful when driving up there.
A pleasant beach along the tip of Port Moresby. Nice houses atop the surrounding hills overlook the beach.
Walking around Port Moresby CBD gives you an idea about how the country is progressing. There are a few highrise glass towers which houses the country's main financial institutions.