If you just have three days to visit Jakarta, come to Bogor as well. Here I give you three days trip to Jakarta and Bogor. I start in Jakarta.
First, visit the National Monument of Jakarta, it is located in the center of Jakarta. From Gambir Railway Station or Gambir Railway Station, you can see the Monument. It is very high, and at the above, which you can reach it by elevator, you can see the city of Jakarta.
After visiting MoNas, then forward to the biggest event of the year in Jakarta, the Jakarta's Anniversary. It is located in Pekan Raya Jakarta, Kemayoran. It would usually held for a month. From around 14 June to 15 July. Open from 11 am to midnight. It's an expo of Jakarta, range from engineering, education, art, property development, and many more. It's a must see event in Jakarta if you visit Jakarta around June and July.
If there's no Pekan Raya Jakarta, I recommend you to visit Jakarta Kota. There are lots of museums over there, like Fatahilah and Bahari. In Bahari Museum (Jl. Pasar Ikan no.1, near Sunda Kelapa Port), you only pay for (around) Rp. 2000 and see some history documentation about Sunda Kelapa. The port, the people, the living, and the ships. There is a tower called Bahari Tower where you can climb up to the top of the tower and see Jakarta, the port and the sea. Quite interesting view of Jakarta.
For hotel, you can stay in Hotel ibis Kemayoran, Jakarta. it is located near the Jakarta Fairground (Pekan Raya Jakarta). You can reach it by taxi.