Partial Differential Equation Toolbox™ has many plot options, such as surface, mesh, contour, and arrow (quiver) plots, hidden or exposed meshes, colormaps, and so on. For command line plotting, see Plot 2-D Solutions and Their Gradients and Plot 3-D Solutions and Their Gradients.
For 2-D PDEs, you also can use the PDE app. The app lets you plot three different solution properties at the same time, using color, height, and vector field plots. You can create plots in the app itself or in separate figures. For details, see Plot the Solution in the PDE App.
For parabolic and hyperbolic equations, you can create an animated movie of the solution. See Wave Equation.