Which is the best exit to take from King's Cross St. Pancras Underground to walk to the German gymnasium?
In reality none of the exits are that far from the gym. From the Circle, Metropolitan, Hammersmith and City line underground station you have two options:
From the exit turn left and then turn right through the shopping arcade and then at the end turn right and exit immediately opposite the gym, this is better than option 2 if it is raining as it is as much under cover as possible,
Turn right out of the station and exit out onto the frontage of King's Cross main line station and then turn left up the road between St Pancras and King's Cross stations, the gym is on your right on the King's Cross side of the road.
From the Victoria and Picadilly line stations follow the exit for the trains and then follow for St Pancras station. When you get through the ticket barrier turn left and go along the passage and up a short escalator, then turn right out of St Pancras station where the gym is directly in front of you across the road. Or as @daniel suggests exit through the ticket barrier and turn right for King's Cross exit and then when you come out at ground level turn right for the gym.