Very much in Europe.
Then, like now, they were the people east of the German speakers.
https://en.wikipedia.org/wiki/Venetic_language :
A 2012 study has suggested that Venetic was a relatively conservative language significantly similar to Celtic, on the basis of morphology, while it occupied an intermediate position between Celtic and Italic, on the basis of phonology
https://en.wikipedia.org/wiki/History_of_Proto-Slavic#Pre-Sl... :
The most archaic Slavic hydronyms are found here, along the middle Dnieper, Pripet and upper Dniester rivers [..] inherited Common Slavic vocabulary [includes] well-developed terminology for inland bodies of water (lakes, river, swamps) and kinds of forest (deciduous and coniferous), for the trees, plants, animals and birds indigenous to the temperate forest zone, and for the fish native to its waters
The fact that the Slavic language seems to have developed inland but the Veneti mostly settled coastal areas puts a big question mark under the Veneti == Slavs link.
But as you say, the rapid transformation of the societies of the groups that migrated at the time is very hard to comprehend, but also the changes of those where they migrated, in cases where it was more of a fusion than an invasion / displacement.
I think it is a very interesting point to offer to those in Europe minimizing the current migration waves (often for noble reasons of reducing racism and countering far right ideologies). It's no use denying that welcoming tens of millions of people from other cultures over a few decades has and will have very deep social and political effects.