I'll be staying at the airport Hilton Hotel and like to go the Forbidden City, can I take subway?

Yes, you can, and you can take Airport Express and transfer to metro line 2 at Dongzhimen. After that, get off Tian’anmen East from Exit A. And then walk north across Tian’anmen Square, and walk for about 30 minutes, you will get there. Or you can take a taxi when you get off of the metro.