Our university's school building is currently under construction on the hillside in the northern part of Fukuoka City.
Literal
Our [attributive-の] university [attributive-の] school-building [topic-は], now Fukuoka-City [attributive-の] northern-part [attributive-の] mountain-side [at-に] under-construction [is-です].
A stack of の particles linking possessive relationships: 僕らの大学の校舎 ('our university's school building'). 建築中 ('under construction') uses the suffix ~中 ('in the middle of'). 山腹 ('mountainside, hillside') is a Sino-Japanese compound. A formal news-like or informational register.