Which institution hosted ARPANET's second node after UCLA?

The institution that hosted ARPANET’s second node after UCLA was the Stanford Research Institute (SRI). SRI’s node connected the network’s first two sites in October 1969.

UCLA hosted the first ARPANET node, with an Interface Message Processor attached to an SDS Sigma 7 computer. SRI’s Augmentation Research Center hosted the second, using an SDS 940 computer running Douglas Engelbart’s NLS system. SRI also became home to the Network Information Center, an early source of ARPANET directories and documentation.

The first attempted login between UCLA and SRI famously failed after the letters “lo” were transmitted and the SRI system crashed. Engineers adjusted the system, and the full login succeeded about an hour later on October 29, 1969. The first permanent link followed in November.

The University of California, Santa Barbara and the University of Utah were the third and fourth sites in the initial four-node network, which was operating by December 5, 1969. Thus, Utah was an early ARPANET node, but not the second one.