I have multiple artists I have recorded. Other than building a website are there any free sites such as sound cloud or sound click (hopefully better) that will let me display the music per artist?

I think Bandcamp is pretty good

I use Sound Cloud, I just like it better than SoundClick, but I'm not familiar with any tools that allow you to organize things by artist other than the ordinary metadata associated with a file. SoundClick looks like it has lots of options but it's just ugly imho. Yes, that matters to me. :) I believe both sites have web page and facebook widgets.
 
There is also Reverb Nation that allows some nice customization and also provides cool music player widgets for web sites and facebook but the free accounts limit file sizes to 8mb unfortunately.
 

Soundcloud seems to be the 'go to' on the Songs forum here at the moment. We (Nettlesmith) have a page there, plus our own website. Personally, I don't like the format on Soundcloud, having a waveform which displays comments from listeners is really odd to me (plus it's back-slap fest, no-one gives constructive criticism)
 
The paid Soundclick pages are much nicer than the freebies. Bandcamp looks OK. Then there's Motagator, Reverbnation, Last.fm, YouTube, Reddit, Bandsintown & Songkick. Plenty of choice now.

Soundcloud is the defacto go to site now.  Soundclick is pretty dated, much like myspace. 

Just worked with both and soundcloud is way easier to use. My old soundclick profile was still there, I attempted to update; very clunky interface.

Bandcamp lets you build a basic artist page and post multiple albums, price per song and per album, post images and other details, and has reasonable fees.  I've use them for years.  I think my sig has a bandcamp link if you want to see what it's like.  

+1 for bandcamp especially if you have albums of work and want to sell at special pricing.
+1 for soundcloud if you want to share unfinished songs in progress or individual songs
 
I'll also give a thumbs up to distrokid if you have albums and artists that you want to get on all the music services, such as itunes, apple music, spotify, google play, deezer, etc. etc. etc. It's a very low cost way to get your music distributed to just about everywhere.
 
One thing that's also hard to figure out is how these services overlap. Bandcamp, soundcloud, and distrokid all play well together and provide somewhat different services. Things like reverbnation provide overlapping pieces that you have to be careful with if you use multiple services.
 
We don't have a soundcloud because we don't usually share unfinished or unpublished works. However, feel free to check out my pages on the other services to get an idea. 
 
https://themoderns1.bandcamp.com/
https://www.reverbnation.com/themodernsus
 
We still have a reverbnation page just because we've had it for a long time and there are a few people who go there. If I were starting now I would just use bandcamp, soundcloud, and distrokid. If you use reverbnation and also use other services, just be sure to configure reverbnation to NOT do the things the other services do for you.
 
There is no page associated with distrokid, it's just a service that gets you distributed to all the online music stores and streaming services.
 
gabo

In the most obscure places I can find.  God forbid anyone I know should hear it, and realize I'm not as good as my recording setup would suggest.  They might start a petition or an intervention....

I hadn't heard of Distrokid, but CDBaby also distributes to all the services for a one time fee per release. They also provide an artist page where people can buy CDs or downloads. I've used them for years and have been very happy with their service.