Ability to easily switch between directories in different areas

For exactly two directories, use cd -

$ cd /tmp
$ cd /var/tmp
$ cd -
/tmp
$ cd -
/var/tmp
$ cd -
/tmp
$ 

Is there anyway I can assign some kind of short name to each one

Yes of course, with the alias command:

alias directoryA='cd /path/to/directoryA'

Then use directoryA as an alias for your cd command. It's really that straightforward ;)

I would use shell variables:

da=/really/long/path/to/directory/a
db=/other/really/long/path/to/directory/b

cd $da
cd $db

The advantage of this method is that you can use $da and $db in place of file paths in any command, for example:

cp $da/file1 $db/file2