How can I get a more traditional drop-down like menu for Unity?

Cardapio is a nice middle-ground between the old and new interfaces:

This screencast shows it in action. The custom launcher available from Web Upd8 makes it quite convenient to use.

It's currently only available from a PPA:

sudo add-apt-repository ppa:cardapio-team/unstable
sudo apt-get update
sudo apt-get install cardapio

Run these commands:

sudo add-apt-repository ppa:diesch/testing
sudo apt-get update
sudo apt-get install classicmenu-indicator

• You can select "Classic Ubuntu" environment at the log-in screen if you prefer classic Ubuntu.
• Optionally, you can get this classic menu indicator: OMG Ubuntu

However, my personal suggestion is to try to get used to it. I didn't like it at first too, but now I love it.

If you right click the Applications icon in the launcher, then you'll get a list of categories like you did in the Applications menu in Gnome-panel. If you select a category, then you'll get a lense with only the applications in that category. You can get the same list of categories if you just click it too. There is a drop down menu on the right of the search field.