Just as the English word "everywhere" comes from two words, "every" and "where," Italian uses the same technique, in many cases. Sometimes the two (or multiple) words become one, such as dappertutto (everywhere).
If we think about it, dappertutto comes from 3 words: the preposition da (from, at, by); the preposition per (for); and tutto (everything, all), an adjective, noun, or pronoun, depending on the context.
I cani cercano dappertutto, ma non riusciamo a trovare nulla.
The dogs are searching everywhere, but we can't find anything.Play Caption
Of course, you don't need to think about the three words making up dappertutto, you just have to remember that it means "everywhere."
In literature, for the most part, we might see the word ove used to mean "where," rather than the word we are familiar with: dove (where). And this leads us to another word for "everywhere": ovunque. We can detect the stem -unque that is part of words like comunque (however), dunque (so, therefore).
Perché non solo la libreria, ma ovunque in città ha avuto danni incredibili.
Because, not just the bookshop, but everywhere in the city had sustained incredible damage.
Captions 63-64, In giro per l'Italia Venezia - Part 2Play Caption
But we can also say dovunque, using the normal word for "where," to mean the same thing.
Vedi il crimine dovunque, anche dove non c'è.
You see crimes all over, even where there aren't any.Play Caption
We can also say ogni dove. This word has remained as two words, which might confuse some people. But if we take it apart, we see the word ogni (each, every) and dove (where).
Per secoli nobili, studiosi, artisti venivano qui da ogni dove per capirne l'essenza.
Over the centuries, noblemen, scholars, and artists came here from all over in order to understand its essence.
Captions 2-3, Meraviglie EP. 1 - Part 1Play Caption