I wonder how many times I've come here with her now.
Literal
She [with-と] here [to-に] come [nominalizer-の][topic-は] how-many-times become [wonder-のだろう].
何回目になるのだろう is a reflective self-question: 'how many times has it been, I wonder.' The のだろう adds a contemplative, introspective quality. A simple but evocative musing — repeated visits to a meaningful place with a partner.