7.) Analyzing the Reactivity of Alkali Metals in Water: An oldie, but also a classic. Metals in group one of the periodic table all have increasingly violent reactions to water. This project makes a good demonstration to get kids hooked on chemistry, although it's advisable to avoid using Cesium. For a science fair project you could talk speculatively about the possible reaction francium, an extremely rare alkali metal, would display.
8.) The Perfect Proportion of Catalysts for [X]: One of the easier projects, try selecting a chemical reaction which requires the use of a catalyst. Then try to determine the ideal proportion of catalyst to reactants.
9.) Demonstrating Conservation of Matter: The Law of Conservation of Matter states that no matter can be created or destroyed, merely changed in form. This can, however, be hard to comprehend. A cost-free science project could focus on showing exactly how this is the case for a certain reaction.
10.) Dopamine and Dating - How Chemicals Make us Feel: Another interesting interaction between two branches of science, this time neurobiology and chemistry. This high school science fair project could be ideal for the intellectual, and possibly slightly aloof, high school student who likes to have a logical explanation for everything.