To the right side by default, it seems to do it right but always leaves me a white space to the left.
Is it possible to set the text close to the left text box's margin? Thanks.
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You can't. That space is always there because of the way fonts are being built. What you can do is adjust this optically via the 'Window → Type & Tables → Story' panel. Enable the 'Optical Margin Alignment' feature and play with the value below until it looks right.
Also look at this question which is similar, but more detail is being given.