Students can see the spectral lines of hydrogen by looking at a arc tube on the lecture table through replica gratings. Several students can come down at once and look. You can also project the spectrum of mercury on a screen for the whole class to see: Projected Mercury and Continuous Spectra [1].
The Frank-Hertz experiment [2] above shows atomic energy levels, but it is a very complicated demonstration.
Finally, a very simple demonstration of energy levels is fluorescent and phosphorescent materials with an ultraviolet light. The energetic UV light kicks the electrons up into high levels, and as they jump part way down immediately (fluorescent) or with some seconds of delay (phosphorescent with partially forbidden transitions), the electrons emit visible light of various colors.
Doppler Shift of sound is dramatically demonstrated by swinging a ringing tuning fork around your head.
The whistle ball is another good way to demonstrate doppler shift. A sponge ball has been stuffed with a battery operated whistle in its core. As the ball is thrown around the lecture hall, the students hear a shift in the ball's frequency.
The action of a diffraction grating itself can be demonstrated by passing a laser beam through the grating and showing the spread out spots on the wall. You can lead into the phenomenon by showing the effect of Single, Double, and Multiple Slits [3] with the Cornell plate. Interesting effects result from crossing two gratings in the laser beam, or by arranging many at all different angles.
A hydrogen arc tube can be viewed with a large holographic grating. Also available is an incandescent light which can be used to look at a continuous spectrum.
Another option is that students can use individual gratings to see the spectral lines of hydrogen.
A hollow prism filled with carbon disulphide will disperse white light into its component colors. Other glass and lucite prisms are available, but their dispersion is not as great as CS2.
A sodium lamp is arranged to shine on a rear projection screen. An ordinary flame, say of a match or Bunsen burner introduced between the lamp and the screen will not cast a shadow, but if a wire or stick dipped in salt solution is placed in the flame, a dark shadow of the flame appears.
Arc tubes of hydrogen, helium, argon, mercury, and a few others can be viewed three-at-a-time with a large holographic grating. Also available is an incandescent light which can be used to look at a continuous spectrum.
Another option is that students can use individual gratings to see spectral lines of these tubes.
A light bulb with a long filament is powered through a variac on the overhead projector. When the filament is turned down, it looks black against the bright light of the overhead. Then the overhead is turned off and it is shown that the filament is actually glowing and emitting light.
Links:
[1] https://demoweb.physics.ucla.edu/node/84
[2] https://demoweb.physics.ucla.edu/node/86
[3] https://demoweb.physics.ucla.edu/node/90