The cost was about 32 million India rupees during the years 1632-1653.
Back then, one rupee was worth 30 Dutch stuivers. Five stuivers were worth 6 British pence. It takes 240 pence to make a British pound.
With this information you can figure that in 1640, one rupee was worth 0.15 British pounds. That means the Taj Mahal cost 4.8 million British pounds in 1640.
Using an inflation calculator for the British pound, I determined that a British pound in 1640 is worth 141 British pounds today. So that means the Taj Mahal cost 678,800,000 of today's British pounds.
Converting that to today's American dollars gives the Taj Mahal a cost in modern American dollars of:
$1,062,834,098