I got Max , but it didn't do my local tax

Not sure what you thought getting MAX has to do with local tax.

WHAT IS MAX

https://ttlc.intuit.com/turbotax-support/en-us/help-article/intuit-product-orders/max/L0Bc4Ve2l_US_en_US?uid=m76e6cmo

TurboTax only prepares a few city or local tax returns as an extra step in your state return.  For most local tax returns you are on your own.  You may have to ask around amongst your neighbors, etc. to find out if you have a local tax and how to pay it. “Google “ local tax for your area.  Call your city government, etc.  Your only record of paying your local tax will be your own bank/credit card records

https://ttlc.intuit.com/turbotax-support/en-us/help-article/tax-return/city-tax-returns-turbotax-state-program/L0fev7XS3_US_en_US?uid=m69jiu1e

How can I see my TurboTax  fees? 

https://ttlc.intuit.com/turbotax-support/en-us/help-article/intuit-account-billing/review-fees-turbotax-online/L1XnIzgzg_US_en_US?uid=m682vq7k

If your TurboTax fees are higher than expected, you can reduce them by removing add-ons     (BEFORE you e-file) :

• Remove Premium Services
• Remove MAX Defend & Restore
• Remove a state
• Remove PLUS Help & Support
• Remove Pay With Your Refund