I don't believe that you can go to the places in your list in one day. Taman Puring, Blok M and Senayan City is in South Jakarta. Plaza Indonesia, Monas and Pacific Hotel is in Cetral Jakarta. ITC Mangga Dua is in North Jakarta. Taman Mini Indonesia Indah is in East Jakarta.
There are TransJakarta busway connects Blok M to Plaza Indonesia/Monas.
Banten is our newest province in Indonesia, formerly belonged to West Java Province.
If u like just laying on the beach, Anyer is the place. U can see the famous Mt. Krakatau from here.
Other optional activities: go to Krakatau, trekking and diving at Ujung Kulon.
Fondest memory: Seeing the sun goes down is my favorite moment. Sunset in Anyer is one of the best I've ever seen.