You can go inside the Sabah State Mosque, though a strict code of conduct is rigidly enforced; you must declare their presence and intention to enter the mosque and must do so through the front door only.
Visit the mosque as part of a Kota Kinabalu sightseeing tour, which transport you between top city sights with ease and let you skip the hassle of car hire. Tours typically tick off the Signal Hill Observatory Platform and Sabah State Museum, which offers insight into the history and culture of the region.
The mosque is centrally located at Jalan Tunku Abdul Raman, which is a 10-minute drive from Kota Kinabalu International Airport. The easiest way to arrive is by taxi, which are offered at economical rates from central KK.
The mosque is open Monday-Thursday and Saturday-Sunday between 8am-12pm and 2pm-5pm. Though the mosque is open on Fridays between 2pm and 5pm, you are discouraged from visiting if you're not there to pray due to Friday being the day of prayer for muslims.
Kota Kinabalu is home to not one but two major mosques, with the other being Kota Kinabalu City Mosque, otherwise known as the Floating Mosque due to the illusion created by the man-made lagoon beneath the landmark. The mosque is best visited at night when its illuminated and the reflection looks most magical.