Hi,
Doing cancer research is a great idea because the disease affects so many people and can be hard to cure. But, as you said, experiments with cancer cells or animals requires expensive equipment and reagents and the equivalent of a university research lab, which few high schools have. You could do this kind of research if you knew someone at a university who would allow you to work in their lab for a few months. Cell culturing and testing of compounds or anticancer therapies requires a lot of time, study and practice to learn the many techniques involved.
You asked what you might do in place of such experiments and I'm afraid your options are pretty limited. You can't do meaningful cancer research on E. coli or Daphnia or bean plants, and science fair rules prohibit use of mammals like mice. There are a lot of online genetic analysis tools and you can download DNA sequence data from Genbank (
https://www.ncbi.nlm.nih.gov/genbank/) that is related to cancer and you might be able to work this into a project for predicting whether a certain drug or compound would be effective against cancer.
Maybe someone else can come up with some ideas for you.
Post again with more questions and I will try to help.
Good luck!
Sybee