I cannot advise you on jazz or lounge bars, but otherwise, I can assure you that Permata Hijau area is one of the most convenient locations in Jakarta. It is very near major protocol roads and the business areas.
Living in an apartment is a good start if you are going to be here for only a few months.
Restaurants, there are many, depending on what cuisine you are into.
There are also many golf courses, problem is, many of the better ones are members only. I am not sure if you can pay additional to get to play in those though...you can always check when you are in town.
There is one short course near Permata Hijau, if you are interested. Not actually tournament standard (too short), but it is very near. And it is Public.
There are some shops available for home improvements like ACE Hardware. Though they are not always complete.
Depending on what you want, sometimes you can order or get them from local hardware shops.
And if you have more questions, you can just write me an email or on this forum.
Hope this helps...