From where are you moving? Jakarta can be quite the culture shock. I can understand your desire to be within walking distance. Your offices in the Plaza Indonesia is located in Central Jakarta and traffic there can become extremely blocked and conjested. You would be wise to avoid taxi or car.
You will probably find that apartments are your best bet, especially as you want to be located close to work. Where will your child be going to school? Is it also nearby? On your budget, you shouldn't struggle to find something to fit your needs.
Many apartment blocks have been built in the city so you will have a wide variety of choices. Since you are settling down with one of your children, living in a villa may not be a necessity at this point. Of course, once you've become used to the city, that is always a possibly you can look into.
However, if you are willing to live outside the city centre, South Jakarta is generally a good place to be. It's there where you will find more houses and villas, as well as a larger international community. Check out our accommodation page for a little more info.
In terms of organising your accommodation, contacting owners or rental agencies online is your best bet. Otherwise, your employer or future employer can hopefully assist.