using 230Volts Hifi components in the Usa

                                              Examples:

            https://www.kccscientific.com/all-products-from-kcc-scientific/

 They (good ones, anyway) can get salty, depending on your device's current draw/consumption.

       Some cassette deck motors run on DC, after power supply conversion and would not be affected.  Others: AC/synchronous.

                                           Best to check!

Yes, plenty of them.  You want a step-up transformer (120 to 240) though, not a step-down.

As a few have already said there are plenty of options for a step-up transformer. I bought a quality one many years ago when I moved to USA and it supplies the Amp, Tuner, CD player and the cassette deck. The system is still working as my second system in my painting studio with no trouble at all. 

Be certain your gear can function properly, at 60 Hz.

                                   Especially: the Cassette Deck’s motor.

Are you certain the motor is AC? I'd expect it to be more likely DC.

You can buy a  used US cassette deck mucho cheaper than a transformer.