Nearness, neighborhood, and propinquity are commonly used of place; approximation, of mathematical calculations and abstract reasoning; we speak of approach to the shore, nearness to the town, approximation to the truth.

J. C. Fernald, English Synonyms and Antonyms (1914)

Example sentences

proximity They want to build a hotel in proximity to the beach.
vicinity We've chosen a hotel in the vicinity of the museum.
approximation It's not the exact value, but rather an approximation.
relationship What is the relationship between politics and war?
affinity They feel a strange affinity with each other.

Popularity over time

Word	1850 → 2019	Trend
propinquity		falling
proximity		rising
vicinity		falling
approximation		falling
nearness		steady
relationship		rising

Use in printed books, per decade from 1850 to 2019.

By length

7 letters: kindred²
8 letters: vicinity⁴, affinity⁴, nearness
9 letters: proximity⁴
10 letters: contiguity
12 letters: relationship⁴, neighborhood³
13 letters: neighbourhood³, approximation⁵, appropinquity

The small number after each word is its number of syllables (kindred² = 2 syllables).