I've found out nested tables in Gmail on iOS tend to break, because it doesn't seem to handle nested tables at all.

I can confirm that "at least" some other developers are having trouble with nested tables, per link given below:

https://stackoverflow.com/questions/31689738/responsive-email-gmail-for-ios-breaks-nested-tables

I wanted to know what are your suggestions for nested tables in Gmail on iPhones, and what to do with it?

Here's a sample HTML email for nested tables. You can see the stock image of Hide the Pain Harold going beyond the outer <table>.

<body>
    <table border="1" cellpadding="0" cellspacing="0" style="width: 654px;max-width:654px;background:#fff;text-align:center;margin:0 auto;table-layout:fixed;border:none;">
        <tr>
            <td style="background:#ffffff;text-align:center;margin:0 auto;table-layout:fixed;padding:0">
                <table style="table-layout: fixed; text-align: center; margin: 0 auto;">
                    <tr>
                        <td style="background-color: #ff0;margin:0;padding:0;">
                                <img border="0" style="display:block;border-style:none;margin:0;border:none;" src="https://i.imgur.com/LSgNMiQ.jpg">
                        </td>
                    </tr>
                </table>
            </td>
        </tr>
    </table>
    <img src="http://click.news.befrugal.com/open.aspx?ffcb10-fec613737462057a-fe2310777467017e731d76-fe901272746c007577-ff2b12797561-fe291570716d0c7e731576-ffcf14" width="1" height="1">
</body>