Find a dedicated server provider and rent the hardware. These companies rent some part of the datacenter (or sometimes build their own). Bonus points if they offer KVM - as in remote console, not the Linux hypervisor. Also ask if they do hardware monitoring and proactively replace the failed parts. All of this is still way cheaper than cloud. Usually with unmetered networking.
Way less hassle. They'll even take your existing stuff and put it into the same rack with the rented hardware.
The difference from cloud, apart from the price, is mainly that they have a sales rep instead of an API. And getting a server may take a from few hours to a few days. But in the end you get the same SSH login details you would get from a cloud provider.
Or, if you really want to just collocate your boxes, the providers offer "remote hands" service, so you can have geo-redundancy or just choose a better deal instead of one that's physically close to your place.