on the cheap

"that would not have to be hooked up to the internet but would work via wi-fi or bluetooth"

Not sure how or what you would be streaming without an internet connection. Did you you mean a hardwire connection? You have to get your content from somewhere, and if not physical media (disks) or a local streaming server ($$$) , then it has to be from the Internet.

Search Amazon for “Bluetooth streamer”. You can get a basic metal box with a blue light which is very reliable, well built, and will likely meet your needs for $60. I have one in my office. I will check the brand tomorrow at work. DM me tomorrow if interested. Works great! 

+5 on the wiim pro

Used Gen1 Sonos players can be found all over craigslist for cheap.

You can also explore a Blue Tooth dongle to hang off the receiver/integrated.

like this

WiiM Pro Plus - fairly often the manufacturer offers refurbs for $149 - just bought one, as my kid stole my other one...they are terrific...and sometimes the WiiM mini for about $60...I’ve only seen these refurbs on ebay from Linkplay (the manufacturer)...

I also bought the WiiM pro + on a discount from Amazon for about 175 for a 3rd system.

even the built in dac is more than acceptable depending on use-case and who’s listening, and what it’s connected to.

Had mine connected via WiFi and plugged into a Vista Audio Spark

Sounded so great all things considered 

I second audiophile1; the Wiim pro +.

My friend installed one in his budget system before Christmas and it sounds absolutely great, especially for the money 👍 No CD storage though (as far as I'm aware)

Amazon. WIIM Mini.
 

https://www.amazon.com/dp/B09HC5GRKY/ref=sspa_mw_detail_1?ie=UTF8&psc=1&sp_csd=d2lkZ2V0TmFtZT1zcF9waG9uZV9kZXRhaWwp13NParams

WiiM Pro Plus has both wifi and Ethernet. Around $200 new on amazon.

Maybe a used Bluesound Node.