I am on an H1b visa in the United States and on my LCA(Labor Condition Application), multiple work locations are mentioned, out of which I work at one of the locations the most. The question is, which city should I be paying the city tax to given that the locations mentioned in the LCA are different cities.
Generally, you pay tax to two sets of jurisdictions:
Where you're resident
Where you perform the work
In the US, most jurisdictions tax their residents on their worldwide income, so if the city you're tax resident of has income tax - it is likely to tax your whole income.
If you are not the tax resident of the city in question, they will only tax your income earned while working there, which means you need to maintain a log where you write down what days you work where, and how much you earned at each place. Year-end - a lot of accounting to do.
Your employer should report each jurisdiction you worked in on your W2 at the end of the year, and you should verify that it matches your log. The tax authority will go by the report on W2.
For most cities that have income taxes, the respective States are tasked with the collection and audits, and the city tax return is part of the State tax return.
In many States, like California, cities are not allowed to impose income taxes at all.
Most cities have no income tax. For those that do, however, the amount of tax you pay will generally depend on how many days you actually work in that city. For example, if you work 25% of your work days in a given city, then roughly 25% of your income will be taxable by that city.
The same principle generally applies to states, too, in case your places of work are in different states.