@tkrunning is right about IB as a place to park EUR without the offshore reporting, but you’re going to pay negative interest rates on that kind of balance no matter what you do or where you go. IB’s rate is currently -0.9% on anything above EUR100k.
If you are convinced of a negative state of affairs, you might consider using one of the currency trading platforms like FXAll or OANDA and simply hedge - buy EUR/USD at 50:1 leverage and just keep enough on deposit to cover margin, which means you can leave the rest of your cash doing something else if you prefer. Current financing is 0%, and no offshore stuff or reporting requirements. You will get taxed on the gain, but you could factor that into your hedge as well and just oversize the hedge such that your expected gain covers the taxes.
Alternatively, you can buy currency options too. OANDA used to do that, but doesn’t seem to any more. CME lists EUR/USD futures under contract “6E” which is a notional EUR125k, and lists options on the futures. Naked calls isn’t the cheapest strategy, of course, but you might do something like buy the long call and sell short dated calls against it or something. But this is just a different level of complexity that I assume you want to avoid.
Of course some would say some of the point of offshore is to have the assets actually off shore, which means finding a bank offshore and going through the whole mess. Obviously there’s reporting requirements. You could go buy property of course and avoid it, or buy physical gold in a vault. But those options are super cumbersome.