I run it on my server in the basement, but you could go for a Digital Ocean droplet, there used to be "one click" installs, but I'm not finding those anymore [0]. There are a lot of tutorials thought you could use. This is my referral link which will get you 10$ and me 25$ [1] (runs a 5$ droplet for 2 months with more than enough specs, if you need more space, that is also easily achieved at DO). Or use this link from Jupiter broadcasting (Linux Unplugged podcast) for a two months 100$ credit [2] (probably there are other codes to getting that 100$ referral discount, this is the one I know).
EDIT: Seems you have to go through a "provider" https://nextcloud.com/providers/
I will investigate further.
EDIT2: OK, so you can can get a Nextcloud instance through one of these providers. Do you have a recommendation?