As a dual EU/US citizen living outside of the US, you may still be required to file taxes in the US and the EU. In general, US citizens are subject to US tax laws regardless of where they live or earn income.

However, as a US citizen living abroad, you may be able to take advantage of certain tax exclusions or deductions, such as the foreign earned income exclusion and foreign tax credit, to minimize your US tax liability. You should consult with a qualified tax professional who is familiar with both US and EU tax laws to determine your tax obligations in both jurisdictions.

In terms of your LLC, it may still make sense to establish one in a tax-favorable state, as this can provide certain legal and financial benefits. However, you should be aware that as a non-resident owner of a US-based LLC, you may still be subject to US tax laws and regulations related to foreign-owned entities.

Whether or not you declare residency outside of the US may impact your tax liabilities in the US and EU. If you establish residency in the EU, you may be subject to EU tax laws and regulations, and you may be able to take advantage of tax incentives or deductions offered in that jurisdiction.

In terms of avoiding taxes, it is important to note that tax avoidance strategies can be complex and may carry significant legal and financial risks. You should always consult with a qualified tax professional before implementing any tax avoidance strategy to ensure that it is legal and appropriate for your situation.