has a lot of those. Kahoolawe was a bombing range, half cleaned up, and now reserved for Hawaiians. Niihau is private and off limits. Ka'ula is still a bombing range. Lehua and many of the other small islands are bird refuges and off limits. Same for all the other NW Hawaiian Islands. And the waters west of Kaua'i are sometimes closed for missile tests (from Pacific Missile Range Facility on Kaua'i) and military exercises (RIMPAC).
Johnston and the other Minor Outlying islands (Kingman, Jarvis, Howland, Baker, etc.) are all bird sanctuaries and off limits. The one exception is Palmyra where I think you can get a permit
Most of the islands around the Southern Ocean that seem unwise to approach: South Sandwich, Bouvet, Crozet, Kerguelen, Heard and McDonald, etc.
I would also stay out of the Paracel and Spratly Islands for a long while.
But I hadn't heard of the Snake Island. That is the most intriguing and scary one I've heard of yet.