Can anyone suggest a free equivalent of the Hoefler Text font?

Assuming it’s the general style you’re looking to match, not exact characters, the key features of Hoefler are:

• The strong, curved serifs
• The quite-high contrast in stroke width
• A moderately high x-height and generally regal and precise shaping.

Garamond is a font that has quite a lot of these features and might be a good stand-in. You probably have a version of it already, and there’s also a variant of it, EB Garamond, on Google Web Fonts, making it free and easy to use online in @font-face if needed.

It’s got similar rounded serifs and similar contrast, but it’s a bit more imprecise in the letter shapes, making it a bit less classically regal and imposing.

Goudy Old Style is another classic old-style serif with similar properties and a variant freely available to use on Google Web Fonts, Sorts Mill Goudy. It’s a bit sharper and more uniformly rounded than Garamond, which makes it a little closer to Hoefler, but it also has a few un-Hoefler-like flourishes (e.g. the spiky ‘horn’ on the lowercase g), and it’s also a little lower in stroke contrast than Hoefler.

If you’re more interested in the heavy ‘classical’ feel of Hoefler than the rounded serifs, Cardo might be worth a look (also freely available on Google Web Fonts). It’s very similar to Hoefler in the shape of the letters and in stroke contrast, and has a similarly serious schoolbook-y feel (it’s designed for “classicists, Biblical scholars” amongst others). It’s serifs are less rounded, but they’re similarly heavy.

As a side note, if you’re looking for a Hoefler-like font for the web, bare in mind that with an exact match, those very rounded serifs and details – particularly the bases of the descenders on characters like ‘p’ – probably won’t render so well on a screen at small sizes.