You can design experiments with ESC and iPSC cell lines. Since cell culture work is easy, I suggest that you look up some differentiation protocols and differentiate your stem cells into a Bering Cardiomyocyte, neurons, skin cells etc. Setting up organotypic cultures esp for skin would be cool as well. If you have mice available, you can also do embryonic development studies. For instance - is differentiation of stem cells cell autonomous or dependent on niche. You can inject ESC at difference embryonic and even adult animal niches and check for their states after few days. If mice is an issue work with Hydra or planarian. You can just cut those things to pieces and study the developmental Biology. Fruit fly is another options.

If you want to keep the experiments in in-vitro format, you can order some yamanaka factor plasmids, some crispr tool kits and study the molecular states of differentiated vs stem cells.

If you are more mathematically inclined, you can make students make morphogen diffusion models, and gene switch models on Matlab. Predict the patterning and see if you can recapitulate any real world examples.

If you have any questions regarding set up of any experiment, just write back. Will be happy to help.