  Hyper-Kamiokande consists of two identical water-Cherenkov detectors of total
520~kt with the first one in Japan at 295~km from the J-PARC neutrino beam with
2.5$^{\textrm{o}}$ Off-Axis Angles (OAAs), and the second one possibly in Korea
in a later stage. Having the second detector in Korea would benefit almost all
areas of neutrino oscillation physics mainly due to longer baselines. There are
several candidate sites in Korea with baselines of 1,000$\sim$1,300~km and OAAs
of 1$^{\textrm{o}}$$\sim$3$^{\textrm{o}}$. We conducted sensitivity studies on
neutrino oscillation physics for a second detector, either in Japan (JD
$\times$ 2) or Korea (JD + KD) and compared the results with a single detector
in Japan. Leptonic CP violation sensitivity is improved especially when the CP
is non-maximally violated. The larger matter effect at Korean candidate sites
significantly enhances sensitivities to non-standard interactions of neutrinos
and mass ordering determination. Current studies indicate the best sensitivity
is obtained at Mt. Bisul (1,088~km baseline, $1.3^\circ$ OAA). Thanks to a
larger (1,000~m) overburden than the first detector site, clear improvements to
sensitivities for solar and supernova relic neutrino searches are expected.
