Tad, where are you staying in Jakarta?
(Jakarta is divided into central, west, east, south, north).

One store worth visiting is Sarinah in Jl. MH Thamrin, central Jakarta. They sell antiques and crafts.

A few miles away from Sarinah is Monas (Monumen Nasional) and Monas public park, the Cathedral and the Istiqlal (biggest Mosque in South East Asia).

Monas pic: http://dailyphoto.org/document.php?id=342

If you go to west Jakarta, there's a section called Kota near the train station. Some buildings in this area still have the old architecture from Dutch colonial era, but they're not in good condition, not well taken care of.

In my opinion, if you're interested in real historical attractions, you have to get out of the capital city. Yogyakarta is a good place to visit.

You have to visit the Borobudur Temple while you're there. Don't forget the Palace. Yogyakarta has a king (sultan).

http://www.buddhanet.net/boro.htm
http://www.bergerfoundation.ch/Home/high_borobudur.html

Fyi, Yogyakarta comes with many pronounciation/spelling. It could be Jogjakarta (Jogja = preferred by locals) or Yogyakarta (Yogya). It's all the same.

Yeah, go to Yogyakarta by plane.

(I'm Indonesian, but have lived in CA for the past 10 years)