Personally I self-host on a raspberry pi. It took me a few weeks to setup, but it has been running without problems for almost 2 years now at practically no cost (beyond purchase and electricity).

Great question. Here's where I've landed:

• For a surprising number of things, my previous desktop, running Linux, confined to my local network, is perfectly fine.
• For a number of other things, a Raspberry Pi, with a dedicated disk image (ISO), confined to my local network, is fine.
• Surprisingly often, a not-at-all-dynamic dynamic DNS solution gets the job done. I follow the first half of the DynDNS guide, and then hard code my preferred IP, and skip the rest. It's inconvenient when my IP changes, but that happens a lot less often than most folks imagine. Most DNS providers have provided this to me for free after I bought my domain name from through them.
• For my public personal portfolio, GitHub pages works fine.
• For additional silly static sites, AWS S3 and AWS CDN get the job done for about $3 per month.
• When I need to do public facing database stuff, I get a virtual private server, not from Amazon or Microsoft, who both way overcharge for small apps.

Plenty of places with $5 per month VPS

I use nearlyfreespeech.net. They bill for usage, and since my site gets almost no hits and doesn't take much storage, it's ridiculously cheap. Much cheaper than even he $2.50.mo VPS listed in another comment. I just checked, and I spend an average of $.30/mo.

VPS' are pretty cheap. Checkout https://buyvm.net starts at like 2.50$/mo

expensive

Highly disagree, but I realize expensiveness is subjective.

What is your definition of not cloud? Does anyone else's VM count? So linode or digitalocean for example would be acceptable, or no?

I guess "alternative" is also subjective.