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Language model tokenizers are typically selected with minimal evaluation, despite the fact that their design choices directly impact model capabilities. This can be partly attributed to a limited understanding of which tokenizer properties affect which aspects of downstream performance. We introduce TokEval, a framework of tokenizer evaluation metrics that goes beyond standard measures like fertility and compression rate to capture linguistically and structurally meaningful properties, e.g., UTF-8 character boundary integrity and digit place-value boundary alignment for mathematics. To validate whether these metrics are predictive of downstream model performance, we conduct controlled language model pretraining experiments, varying solely the tokenizers' training data mixture, pretokenization strategy, and training algorithm. We evaluate the resulting models on bits-per-byte and several targeted benchmarks, spanning linguistic understanding, mathematical reasoning, and code generation. Our experiments show a division of labor among intrinsic metrics: information-theoretic metrics predict perplexity-class outcomes (Spearman correlation up to 0.80), while only structure-sensitive metrics, such as those measuring digit and line-break handling, predict task accuracy. We hope TokEval enables more principled tokenizer evaluation, replacing pretraining sweeps with intrinsic measurement wherever the two agree.