Download VEP and run via the command line. It takes VCF files of any size, offering multithreading (forking) and plenty of options to customize the annotation (the Web version does as well of course). It can be installed by
conda to save you from getting all the dependencies and perl extensions manually.
SnpEff is probably the other most comprehensive one. Though as @ATpoint said, you can also just run VEP from the command line (SnpEff must be run from the command line anyway, but it has more regulatory annotations than VEP if you're interested in non-coding variants).