What is the approx. cost for taxi and also black cab from Capital Airport to Ramada Beijing North?

Nicole, your hotel is located in the northern suburb area of Beijing. I'm afraid most taxi drivers and black cab drivers are not willing to go this far.
Actually, you can take airport shuttle bus line 8 to Huilongguan (Longze) at a cost of CNY24. Then, take a taxi to your hotel for a fare of CNY20.
Both shuttle bus and taxi only accept cash. Make sure you prepare some cash.
Oh, most taxi drivers can speak simple English, but it is still suggested you translate the name of your hotel '龙城华美达酒店' in advance and show it to the driver.