From the PDE app you can use plot mode, where you have a wide range of visualization possibilities. You can visualize both inside the PDE app and in separate figures. You can plot three different solution properties at the same time, using color, height, and vector field plots.
Surface, mesh, contour, and arrow (quiver) plots are available. For surface plots, you can choose between interpolated and flat rendering schemes. The mesh may be hidden or exposed in all plot types.
For parabolic and hyperbolic equations, you can even produce an animated movie of the solution's time dependence. All visualization functions are also accessible from the command line.