What is the best way for a family member to repay a loan over $15,000.00 to me without having to pay taxes?

Your family member does not owe any tax when repaying a loan.  Simply transfer the money by any convenient method.  If you are thinking about the requirement that banks must report transfers of more than $10,000, this is just a reporting requirement and no tax is owed.  And, if you structure the transfer into several small amounts to avoid the reporting rules, this can sometimes constitute a crime called "structuring" even if the actual business is legal.

However, as the lender, you are required to pay income tax on the interest you received or could have received (even if you did not charge interest).  The IRS expects taxpayers to conduct their affairs in a businesslike manner and that includes charging interest.  You need to charge at least the applicable federal minimum interest rate.

https://www.irs.gov/applicable-federal-rates

For example, suppose you made the loan in December 2022 with a 1 year term, the applicable interest rate was 4.55%.  That means that you must pay income tax on $682.50 of interest that you could have charged, even if you didn't charge interest.  You would report this as interest income without a 1099-INT on your tax return.

Here's a blog post about it.

https://turbotax.intuit.com/tax-tips/tax-payments/irs-tax-rules-for-imputed-interest/L7UbulHpC