Roaring Heights dowloaded, but does not appear in game

I believe you have to click it , like you would when downloading custom content. Find it in your downloads folder and click it [hope this helps]

Are you talking about the check mark box in the downloading area on sims? Yes I did do that and on the status it says installed (well it doesn't say that, but a blue arrow pointing down to a pack of cards with the green sims gem on it). When I start to play my game though none of the worlds appear. Like when I create a new game and have to pick a town none of those come up.

Try this from the Store FAQ

I installed my Store Content but it's not showing up in my game

Unfortunatly, the Launcher is a very unreliable tool. The more stuff you have, the greater the chance that files which have your stuff installed get messed up. If that starts happening to you. It's best ro reinstall all Store content, using this method:

• Close your game and launcher
• Go to documents\electronicarts\thesims3 and move the folder DCCache to your desktop (this is ALL your custom content, so if you have 3rd party content as well, you might wanna just move the *.ebc files as well as the missingdeps.idx)
• If you have any worlds installed go to the installedWorlds folder and delete all Store worlds from there.
• Go to the DCBackup folder and delete everything in there. You don't really need the stuff in here except for the ccmerged file but since you're reinstalling everything, it will be recreated.
• Open the launcher and start reinstalling all store stuff in groups. Don't install all in one go. Start with the worlds, then lots, then sets and single items last.

When you're done, backup the DCCache folder. If the same starts happening again, go back to that backup so you don't need to start over. Make a backup from time to time, especially after you've installed worlds and lots.

No this does not work I also tried uninstalling everything and reinstalling it, but the worlds still are not showing up.

I am having the exact same problem with the exact same worlds and no matter what I do they will not show up in the Main Menu or Launcher.  I believe I'm done with Sims since it just doesn't work anymore.  Sad thing, I just dropped cash on one of these worlds yesterday and all it did was louse up my game.  Thanks a lot EA!

Try resetting your user files as described in the factory reset described in this post: http://answers.ea.com/t5/The-Sims-3/FAQ-Troubleshooting-Steps/td-p/714/

You won't loose anything. Just make sure to not delete any files  and make a backup.

Then just install Roarding Heights and test if it works.