@echo off
set /p Dir=Enter directory name:
:check
if exist \%Dir% goto blocked
md \%Dir%
::copying goes here
goto exit
:blocked
cls
set /p Dir=Directory already exists. Enter new directory name:
goto check
:exit
Ok, that asks for the directory name, then makes it at the root directory (most likely C:\, but you can change where it's going to be saved). It also checks if that directory is already made, and if so asks for a new name. The ::copying goes here is where your copy code goes. I don't know where your eventlogs are located, but just write:
copy "your eventlog location" \%Dir%