The Soviet Union launched its space flights from the Baikonur Cosmodrome in Kazakhstan’s desert steppe of Baikonur, (remember Sputnik 1?), and it’s still used for launches to the International Space Station.
Though bureaucratic and expensive, it is possible to get permission to enter the cosmodrome, watch a launch, and visit the on-site museums with their collections of space craft and related technologies.
That said, if you’re travelling on a budget, it might be easier to park your vehicle some distance off and watch the spectacle unfold in the sky from there.