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We use dynamical systems approach and Lagrangian tools to study surface transport and mixing of water masses in a selected coastal region of the Japan Sea with moving mesoscale eddies associated with the Primorskoye Current. Lagrangian trajectories are computed for a large number of particles in an interpolated velocity field generated by a numerical regional multi-layer eddy-resolving circulation model. We compute finite-time Lyapunov exponents for a comparatively long period of time by the method developed and plot the Lyapunov synoptic map quantifying surface transport and mixing in that region. This map uncovers the striking flow structures along the coast with a mesoscale eddy street and repelling material lines. We propose new Lagrangian diagnostic tools --- the time of exit of particles off a selected box, the number of changes of the sign of zonal and meridional velocities --- to study transport and mixing by a pair of strongly interacting eddies often visible at sea-surface temperature satellite images in that region. We develop a technique to track evolution of clusters of particles, streaklines and material lines. The Lagrangian tools used allow us to reveal mesoscale eddies and their structure, to track different phases of the coastal flow, to find inhomogeneous character of transport and mixing on mesoscales and submesoscales and to quantify mixing by the values of exit times and the number of times particles wind around the eddy's center

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