I can't find an exact age, but with some assumptions it can be narrowed down. In Rascals (ST:TNG season 6), set in 2369, we have the following conversation:
"Look at these fragments. They're… they're very nearly in perfect condition, and yet they're seven hundred years old."
"So is my father."
— Picard and Guinan
700 may not be a precise figure, but assuming Guinan is rounding, he's nearer 700 than 800. If we also assume he didn't have children before age 20 (again, nothing to confirm but a life expectancy of centuries – seems plausible). This makes her 730 as an upper bound. As @ruakh points out in the comments, if she was 700+ herself, she would likely use herself as the comparator and not her father, so she's under 700.
In 1893 she is an adult and not on her own world. She comes across as having some life experience; even with the knowledge of an advanced race she doesn't seemed fazed by the experience. This makes her at least 500 by the time of TNG.
Non-canon novel 'The buried age' https://memory-beta.fandom.com/wiki/The_Buried_Age suggests she is on Earth after spending her 'early 100s' travelling – this would put the lower estimate at around 600; this also seems more in keeping with her personality and experience, but I can't find a canon reference.
Best estimate 600–700.