This has annoyed me for a while too! On my hunt for a solution, i found this post and thought i'd post the solution i've come up with to tackle it.
We can't get Adobe to put the folder anywhere else (i.e. /Library/...), but we can hide the folder by changing the chflags
.
Type the following into the terminal to hide the folder. (It'll still be there, just hidden.)
chflags hidden ~/Documents/Adobe
If for whatever reason, you want it visible again, just do this:
chflags nohidden ~/Documents/Adobe