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Synapses likely change their strengths based on a form of spike-timing-dependent plasticity. Is this true for all types of synapses in all parts of the human brain?

No, not all. For example, there is frequency-dependent-plasticity, where the firing frequency of the pre-synaptic cell will change the synaptic strength. In Nikolaev, et. al. (2013), frequencies below ~5Hz will depress the synapse, while those above 5Hz will facilitate.

I wonder if there are also synapses with hard-wired connectivity, i.e. that does not does not depend on the activations of nearby neurons or does not change at all.

It's possible that there might be, after all, you're talking about a complex object like the human brain. Though, this may be very rare. For example, even electrical synapses, or gap junctions, appear to exhibit plasticity. In Fig 6 of Pereda et. al. (2012), you can see how the conductance of the gap junctions is altered by the activity of nearby cells.