遠い and 近い: distance and approaching times
Compare reference points for distance with approaching events, and examine the structures 近い駅 and 駅の近く.
Far from or near to where
家から学校までは遠いです。 says that school is far from home. 遠い, read とおい, becomes clear when the reference point and destination are identified.
このホテルは駅に近いです。 says that the hotel is near the station. に with 近い, read ちかい, marks the location used as a reference.
Before nouns and in location phrases
ここから近い店を探しています。 says that someone is looking for a nearby shop. 近い directly modifies 店; do not add な to make 近いな店.
駅の近くに店があります。 says that there is a shop near the station. This location structure uses 近く, not 駅の近いに.
Closeness in time
試験の日が近いので、復習しています。 says that the speaker is reviewing because the exam date is near. It concerns an approaching time, not physical distance.
遠い昔の話です。 describes a story from the distant past. 遠い can apply to time, but it does not specify an exact number of years.
What does 近く express in 駅の近くに店があります?
Show the answer and why
It expresses the area near the station. The shop is nearby; the adjective 近い is not placed directly before に in this structure.