If hydro is available, why not use it? Nothing is perfect by any means, but once the dam is constructed, hydro is a relatively inexpensive source of constant, high quality electricity 24/7. A good example of this would be Paraguay/Brazil's Itaipu Dam.
If it were available, I'd definitely go hydro. However, in a lot of areas, it definitely isn't going to be possible.
Most likely, a data center would probably have to use a mixture of sources. Solar would definitely help take the edge off peak energy consumption (both in the energy machines used, as well as the energy used by the HVAC system to keep them cool.) Next to that, a wind farm (although not many areas in the US are good for this.)
If the data center is in a completely rural area, what might be one source, assuming the absolute stark terror of nuclear abates for a bit, using an on-premises thorium reactor (LFTR/MSR as a type as it can use more generated energy, as per the Transatomic ads... take them with a grain of salt) comes to mind. This would not just provide base energy for the data center, but also be an asset to the electric grid.
Of course, if fusion power becomes available, all the debate about energy becomes moot.