I see that long-term capital gains tax rates are 0%, 15% or 20%. But these are federal so is there also a state and local tax on long term capital gains? Specifically in New York City, which for ordinary income subjects to a local NYC tax and NY state tax.
New York State income tax makes no distinction between capital gain income (long or short) and earned (wage) income.
As you've noted New York City has an additional income tax on top of the New York State income tax.
The State And Local Tax (SALT) deduction applies to the Federal itemized deduction, and starting for the 2018 tax year capped at $10,000 USD. As noted in the media, the cap hit individuals in high tax states the hardest as the cap applies to both state income tax and property tax combined. Where those individual were able to deduct from their Federal AGI more than $10K in the past, it is now capped at $10K meaning more Federal AGI and therefore more Federal tax paid.