"let's meet up" is a common usage
throughout the British isles
Two things wrong here. Firstly 'We can meet up anywhere' - the 'up' is redundant and not used in British English. Secondly 'Anywhere' is not a synonym of 'Everywhere'. It's subtle, and is similar to the relationship between the definite and indefinite article. Anywhere suggests a specific known place picked from a random a choice of locations. Everywhere is an unknown place at choosen at random. It also suggests simultaneity. That is we meet at every place at the same time.