What are the tax implications if my sister gives me 60K towards a house so that I can pay cash and I plan on paying her back over 3 years?

Your sister is giving you a loan. The terms of the loan should be written and signed by both of you. If you pay her interest on the loan she would pay tax on that amount in the year it is received.

If you do not pay interest, your sister is still required to report as income a minimum amount of imputed interest:

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

If the loan is secured by your house (i.e. it is a mortgage loan) and it is officially recorded as a mortgage loan, you can claim a tax deduction for the interest that you pay if you itemize deductions.