For those of your clients who requested website overhauls, they'll probably prefer to keep their new websites on the same location, as their own hosting, usually it's a cPanel hosting account, like HostGator or GoDaddy, so WordPress is a first choice, if you (and they?) enjoy using it.
But as you mentioned they're local businesses, with limited budget and needs for basic web presence, they would probably love to manage their websites on their own and WordPress may look scary for most of the less technical users. You can try Kopage (https://kopage.com), similar to WordPress, it can be self-hosted, but it works in the cloud in the first place. And it's free.
A little disclaimer: Kopage is one of my projects, and this was the exact reason it was created in the first place, as a tool as user-friendly and intuitive as possible for our own clients, so they can manage their own websites and don't be afraid to break something.
There's a white-label plan if you'd like to offer it under your own brand.
There's a quick, live demo on the website + an installer, single PHP file to [1] upload to any hosting account, [2] open file in the browser, [3] installation & setup will start automatically.