on the cheap

Can't believe how many here gave the OP a hard time about the Ethernet/WiFi connection. I know y'all know what he meant..no physical connection, WiFi. He's looking for the cheapest streaming option for his sister that is obviously no "audiophile", will probably never purchase a hi res streaming service, and no interest in an external DAC that will cost more than the streaming device. Obviously your not going to find a CD storage device, streamer, Bluetooth, DAC for under $200. She probably just needs a Bluetooth device..but since dac is needed as well a WiiM is most likely the best option. 

For your sister with no real HiFi aspirations an $80 WiiM Mini should do the trick. You could go up to the a pro at $150 for a better DAC but also rca outputs instead of the 3.5mm of the Mini. 

+1. @mattw73   

 Do the Wii have built in storage?

@mahler123 unfortunately no.  Maybe some one has heard of a model with storage in a "budget-ish" range but I can't think of any. Internal storage is normally found on some of the more or most expensive units. The next best thing I guess would be to have a streamer with a  USB port to play your downloaded/stored music files. 

The next best thing is iphone with the adapter and usb hub like these

https://www.amazon.com/dp/B0BZRYKSF5?psc=1&ref=ppx_yo2ov_dt_b_product_details

https://www.amazon.com/dp/B083XTKV8V?psc=1&ref=ppx_yo2ov_dt_b_product_details

@mattw73 

the Op mentioned that his sister might want included storage.  It was unclear if he meant rip and store which bumps the price tags a few hundred bucks.  If she already has storage on a flash or separate hard drive then that wouldn’t effect the price tag