najbaro

Straightforward, and the affixes do the rest: najbarino a female neighbour, najbara neighbouring, najbareco the state of being neighbours, najbaraĵo the neighbourhood as a place. Note that the adjective is genuinely useful in Esperanto where English would reach for a different word entirely - la najbara lando is the country next door, la najbara ĉambro the room next door. The -aj- in the middle is a diphthong, nigh-BAH-ro, so it is one syllable and not two.