Day of Two Suns by Jane Dibblin (1988) — The definitive account of nuclear testing in the Marshall Islands and its catastrophic consequences for the Marshallese people. Focuses on Bikini and Rongelap atolls but provides essential context for understanding the broader US military relationship with the islands, including Kwajalein.
History of United States Naval Operations in World War II, Vol. VII: Aleutians, Gilberts and Marshalls by Samuel Eliot Morison (1951) — Morison's authoritative naval history covers Operation Flintlock, the February 1944 assault on Kwajalein, in detail. Essential reading if you want to understand what you're looking at when diving the lagoon wrecks.
Micronesia by David Stanley — Part of Moon Handbooks' Pacific series, this is the most comprehensive English-language travel guide to the region, including the Marshall Islands. Useful for planning the parts of Micronesia that are actually accessible to independent travellers.
PCT: Paradise or Purgatory? American Military Basing in the Pacific — Various academic works examine the political economy of US basing arrangements in the Pacific, of which Kwajalein is one of the most contentious examples. The Compact of Free Association, which governs the US-Marshall Islands relationship, is worth understanding before visiting.