For $\mathbb{R}P^2$, I like [Boy's surface][1], which is a particularly symmetric immersion of the projective plane into $\mathbb{R}^3$.

Also, see [this][2] Java-based model.

You can build a piecewise-linear version of one of these out of paper.  If you cut out a disk-shaped window (to see inside to the triple point), what you have is a model of the Mobius band for which the boundary circle is really a round circle!

Of course, this doesn't really help with all of the rest of them $(n \ge 3)$!


  [1]: http://en.wikipedia.org/wiki/Boy%2527s_surface
  [2]: http://www.physics.unc.edu/~amellnik/surfaces/boy_jv.html