it's pretty hard looking for a app. if your not yet in jakarta cause the app. on the internet are limited. If you are in jakrta, you can better stay a few days in a hotel and from there you search. There are a lot of app. in the center of jakarta, depends on your budget. You have the Taman Rasuna app. A friend of mine just rented a 2 bedroom app. there for 6 million rupiah a month. That's just about 500,- euro's. excluded water/electr/maintanance. You have a swimmingpool,basketballfield etc.
There is also the kuningan app. which start from 1000,- euro's/month. They are managed by the Accor Group.
Behind the WTC there is an area where there are a lot of deluxe rooms for rent. Just get a cab and drive though it. Some of them are really nice and start from 1 to 2,8 million/month. I just checked them out myself. If you are in Jakarta buy the Poskota and Kompas. These papers have a lot of app. for rent.