If you are a US citizen and have an accessible US address, you probably can open a Schwab or Vanguard account or an account with most US financial institutions that let you open accounts online and don't care where your IP address says you are (so far only US HSBC has cared in my limited experience).
If you invest with an institution outside of the US you'll have to deal with 30% US tax withholding, but some threads have ideas with bringing that down to 15% with I think Irish domiciled ETFs (I haven't tried this myself).
So what works best also depends if you're a US citizen or not.