Yes, its 110,000 QF FF points for an economy class award flight MEL-LAX-JFK and return. However, as you plan to stopover at more than just New Yrok, you will also be charged 10,000 points per stopover. So a stopover in LA in one direction will cost a total of 120,000 points. I would recommend driving LAX-SAN - its not very far.
Also note that the rules and points for award flights changes in May. So book early as these types of awards will cost significantly more points after May.
I would strongly recommend you plan to travel LAX-JFK and return on days that QF operates QF107/108. You will be the usual in-flight entertainment and catering for QF international flights on 747-400 aircraft. If you use an AA flight you will not get personal IFE, just a shared big screen and will have to buy your headphones from AA. And they are even rumoured to be sgtopping catering on AA trans-continental flights. Also note that the QF operates flights LAX-JFK-LAX are unlikely to be filled so more room to spread around.
You can upgrade on QF flights, both nowe and after the May changes come into place. The difference is that after May the upgrade will not be confirmed prior to check-in. You will need tpo waitlist. But you can only upgrade to business class with points or upgrade credits if you have a confirmed and paid economy class ticket. After May you can not upgrade the cheapest of the fare classes (such as N class). Prior to May you can upgrade any paid economy fare.
Whether its better to buy a ticket of reddem for points is a personal decision only you can make. What value do you put on your points and do you want to save them for a specific purpose? Do you need the status credits from a paid fare to reach or retain a FF status level? Remember that it is generally agreed that points will lose some value with the changes to the program in May (some may say that is a vast understatement, but I am trying remain objecting and unemotive).
Taxes and charges will be the same for an award ticket as they would be for a paid ticket. Only a travel agent of Qantas can tell you exactly how much that will be. Expect them to be in the order of $280-300 depending on the stopovers and flights taken.
Time at each place depends on what you want to do and see as well as your budget. Again, only you can answer that question.
