This is a city of many names. In the last 100 years it has been known as different things, first it was called Hollandia, then Kotabaru (new city), and then Sukarnopura, and even Port Numbai, but today we know it as Jayapura. The City stands Looking down upon the Bay. There is a tourist industry in Jayapura yet it is small, as most people use this for a jumping off point.
Of course as in many destinations Shopping is a fundamental and enjoyable Pastime. This is also true here plus there's the added bonus of a very unique souvenirs. The original people of this area are known as the Asmat and they are famous for their woodcarvings. So there are many amazing opportunities to collect unique stylised elaborate woodcarvings. The original intent of these woodcarvings was to honour ancestors that is why these would make a perfect gift for family members. Check out the shops at Hamadi.
Now, you might be sad to hear or overjoyed to hear that there are only a couple of fast food western outlets in the city that means you will enjoy some of the best local seafood available. Places for you to go and enjoy are actually a little bit limited as this is primarily an industrial town. However if you're prepared to jump in the car and go for a little drive you can encounter some beautiful beaches such as Holtekamp Beach. It will take you around 30 minutes to get there.
Other things to do while you are in the area would be to Check out sentani lake which is about 20 km south-west of the city. For most of these places it is very different than other island in Indonesia you will need to bring your own drinks and possibly food with you, as they will be very few facilities for tourists.
Plus if you're lucky enough to visit in August you have to check out the Lembah Baliem Cultural Festival. This is a great way to see the true culture first-hand.