I am planning to spend 3-4 months in Jakarta, with my little family (wife and kid) I don't want to stay in a hotel for this long, I heard there are nice apartments with reasonable prices in Jakarta (2 rooms, Toilet and kitchen) for monthly rent. Any suggestions on where to find that?
Based on your budget, it's quite difficult to rent a service Apartment.
The only way to go is to rent the apartment from the owner directly. You can try Roomorama or AirBnb for this. If you click on the Rates tab, both website also provide monthly rent rates. Personally I think you may get a better luck with Roomorama.
However you may want to top up a little since the one I saw have rate around 600-700 USD/month.
3-4 months is too short for most rental agencies, which means your best option is probably going to be a service apartment. Plenty of choices (Ascott, Oakwood, Somerset etc), just Google around.
The first and most important question is, where will you be spending your days in Jakarta? The traffic is astonishingly terrible and you want to stay as close to your place of work as possible. Many expats favor the Kuningan area, which has plenty of modern accommodation and is close to the main business districts.