Mukta Malar is a good example of a modern Tamil font and is available in
google fonts. I reproduce the details about the font: "Mukta is a Unicode compliant, versatile, contemporary, humanist, mono-linear typeface family available in seven weights, supporting Devanagari, Gujarati, Gurumukhi, Tamil and Latin scripts. This type family is a libre licensed version of Ek's self-titled multi-script project, an ongoing effort to develop a unified type family for each Indian script." Mukta Malar supports Tamil. in my experience, I find this font pleasing to the eye. It must be good both for print and display.