in your question you cite two different things: genotoxicity and neurotoxicity. Genotoxicity tests are dedicated principally to assess occurring mutagenesis after exposition of living cells or organisms to genotoxics . From theses, you have; mutatest of Ames, tests on cells in culture, tests on drosophilia melanogaster, tests on specific mouse strains,... However these tests do not allow to assess toxic effects on brain. You can refer to conventional toxicological tests (acute, sub acute and long term toxicology).
In your question you involve three different terms which we need to clarify: toxicity, cytotoxicity and genotoxicity.
When we talk about toxicity, it is related to damages to whole organisms, mainly, while cytotoxicity is related to damages to the cells, which could be, for example, neurons. Genotoxicity is related to damages to the DNA of the cells, which could result in mutation (mutagenicicity) if the cell not repair the damage and this is fixed.
By these terms you could chose the best assessment, as follows as example:
Toxicity: as already mentioned, could be acute, subacute or chronic exposure, according to the chosen species (e.g. Danio rerio, zebrafish);
Cytotoxicity: by a cell culture, you could perform a MTT test, to assess this endpoint;
Genotoxicity: the most used technique is comet assay, which could be used with cell culture or cells from a tissue.
I suggest you look for a Toxicology book, because it will define all terms. In the literature you also could find some papers about neurotoxicity and its evaluation, like bellow:
Kulig BM. Comprehensive neurotoxicity assessment. Environmental Health Perspectives. 1996;104(Suppl 2):317-322.
Chuenlei Parng, Nicole Marie Roy, Christopher Ton, Yingxin Lin, Patricia McGrath, Neurotoxicity assessment using zebrafish, Journal of Pharmacological and Toxicological Methods, Volume 55, Issue 1, January–February 2007, Pages 103-112, ISSN 1056-8719, http://dx.doi.org/10.1016/j.vascn.2006.04.004.
I agree with Ali Saeed, Aida and Roberto, the tests are explained, Comet assay is best for determining single cell DNA damage, and MTT assay is good for determining LD50 and LC50. Roberto has given details - please follow.
Relative to genotoxicity assessment, in addition to the several suggestions for the comet assay, you might also consider looking at gamma-H2AX foci as an indicator of DNA double strand break repair foci. Depending on your tissue preparation and available instruments, you can look at this in dissociated whole cells or tissue slices. This might nicely complement/support any results you see from comet analyses. Keep in mind that all these suggested tests would be responsive to clastogens that are breaking DNA, if you are potentially looking at an aneugenic mode of genotoxicity you will need other tests such as CREST or centromere staining.
I'm seeing both frozen and FFPE-based methods used for H2AX analyses. Here's a link to a paper that describes both in the methods section. I'm sure if you dug around you could find more examples.
If you decide to perform comet assay in that brain cells, but if you work with in vivo cells, an oustanding aspect you have to look close is the disagregation method, because if you harm cells during that part of the process, a significant amount of damage could arise. This is obvious but in my experience with mice brain cells disagregation is critical.