I believe that a number of the air-ground rockets, such as the 5" FFAR & HVAR and the 'Tiny Tim' were developed at the Naval Ordinance Test Center at China Lake in California's Mojave Desert. The various versions of the 'Bazooka' were initially developed as prototypes in labs at George Washington University, and developed into servicable weapons at the Army's Aberdeen Proving Grounds in Maryland.
As for artillery rockets, in addition to ship & vehicle mounted variants of the FFAR & HVAR, the Navy & Marines used a 4.5" bombardment rocket also developed at China Lake derived from the
'Mousetrap' ASW launcher used by the Navy (comprable to the 'Hedgehog', but very dangerous- the destroyer
Turner and destroyer escort
Solar were both sunk with heavy loss of life by massive explosions believed to be caused by malfunctioning Mousetraps. The Army had a 7.2" demolition rocket, also derived from the 'Mousetrap,' and developed at China Lake. In addition, the Army had 4.5" bombardment rockets, but I haven't seen anything as to where they were tested, although either China Lake or Aberdeen would be my guesses.