Solution: (1) The table tennis hall is located at (3,4), in the southeast direction of the swimming pool, at an angle of 45 with the horizontal line.

(2) The position of the tennis court is (5, 5).

(3) The location of the bowling alley is (2 1), the northeast of which is about 30, and the archery alley is about134.2m. 。

(4) The positions (3, 7) of the fitness center are drawn with black dots as follows:

(5) Xiaoming and his father took the route of (3,4) → (2, 1 )→ (1, 6) in the fitness center. They went to the table tennis hall, bowling alley and swimming pool.

So the answer is: (3,4), southeast, 45. (5,5).？ (2, 1),30 , 134.2.(3,7).