The best replacement for bodoni is didot.

The best alternatives to bodoni are rated as following:
★★★★★  didot
★★★  baskerville
★  bauer bodoni

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Speaking about bodoni, one probably shouldn't forget about sans serif.

Other search terms related to bodoni and their ratings are:
★★★★★ sans serif
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Google Trends

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bodoni
didot
baskerville