Keep the NAD C370! It is an excellently built piece of audio gear. They actually don’t make a lot of mid-level stuff like this anymore.
http://cd8ba0b44a15c10065fd-24461f391e20b7336331d5789078af53.r23.cf1.rackcdn.com/polkaudio.vanillafo...
If you have concerns about the age of the NAD C370, I would maybe ask a DIY friend or an electronic repair shop to replace some of the electrolytic caps inside. At this point, the caps are probably pretty aged out. Replace them with something good like Elna Cerafines, or even Nichicon. It will turn the NAD into something excellent (though I’m sure it’s great as it is).
I used a Krell HTS 7.1 processor for 13 years and, even though it’s considered "obsolete", it still beat the crap out of a lot of stuff I have reviewed. The "audio" portions of this type of equipment generally cannot get better. It’s the "digital" or "feature" stuff (hdmi, blu-ray, etc.) that tend to be looked at as "outdated".
The NAD tuner you can keep as a good item if you continue to listen to AM/FM.
The Marantz AVR is definitely outdated (as far as features, digital/hdmi support, bluray, etc.) but can still be used. The older Marantz stuff did have good sound, but it had a warm/slow signature that could be taken as "boring". The new generation Marantz equipment is definitely improved with differently designed circuits.
I don’t know a lot of details about Sonos, but after briefly looking at the technology, I think your NAD integrated is still going to produce a much better sound quality than anything Sonos. I think a product like Sonos is going to cater more to the "iPhone generation" and not necessarily to any type of audiophile.
I would keep the NAD stuff and maybe look into something like a Marantz network audio player (NA6005 or NA8005). They can stream from Spotify, internet radio, Apple Airplay as well as from any DLNA source. You can setup Jriver on your computer to use as a music source. It will play a multitude of different file types and the Marantz has excellent audio quality (fully discrete audio stages, etc). I think this will pretty much blow the Sonos stuff out of the water with regards to sound quality.
Alternatively, you can look at the Marantz bluray players. They will support DLNA/JRiver servers and also will play CD/SACD or bluray audio. But it doesn’t look like they support the internet audio/radio stuff.