We are arriving at Tianjin on a cruise ship and would like to see the Forbidden City in Beijing....

I'm afraid it's difficult to hire a regular taxi to travel that far. Maybe you need to hire a private bus and it would cost you around CNY 1000-2000 based on vehicle type.

Or you may try to contact this website to see if they can organize such an itinerary for you. This is their contact info: traveltravelchinaguide.com

You are suggested to take a taxi to get to South Railway Station first. The cab fare is about CNY 200. Then take bullet train to get to Beijing South Railway Station first. It takes around half an hour on the way. The ticket fare of second class seat is CNY54.5 and first class seat is CNY94.5.

After arriving, you can take a taxi to the Forbidden City. It costs around CNY 25. In addition, the last train returns to TJ from Beijing South Railway Station is scheduled at 19:00.