Jakarta - where to stay, what to do?

I'm going to be in Jakarta for several days next month, and I've found the Wikitravel article to be as many describe the city - immense, with many sights, jams, and back corners. Does anyone have any suggestions on places to stay? I'm looking more for areas rather than specific hostels. I'm planning on staying in a guest house or hostel, preferably near something interesting to do or see. I'm fine with cheaper accommodation as long as it isn't insanely seedy or out of the way. I'd also love suggestions on good areas to explore, especially for someone who enjoys food. I'm from the US, but I love new and exiting foods, so I'm open to any array of different styles. Finally, I'll be heading to the southern half of Sumatra after Jakarta - any thoughts on what to see? Thanks for any info.

Edit: You guys are awesome, thanks for all of the helpful info.