I'm no expert in US tax law, but Romania and Bulgaria are pretty business friendly. You pay 5% tax on dividents and 3% corporate tax. You pay 1% if you have an employee. That is all you pay, no VAT, no other extra tax. That's all you legally pay. You can withdraw money from the business every 3 months. Accounting expenses are around 25$/month. The place is part of the EU and with lower crime rates than Japan. To have somebody do the paperwork and open you the business, it will cost you 100$.
We're standing at 12k GDP per capita, up from 1.5k in the 90s. It's not a hellhole anymore like non-EU eastern europe. I can phone my lawyer and ask how much it would cost you and whether there is a problem that you're not from the EU.