How can I run an iOS or Android app on my PC?

I've got a SWTOR account, and I'm interested in adding a security key to my account. Not because I'm particularly worried about my account being compromised, but because it allows access to a particular vendor in game as an incentive to increase your security.

Since the app is free, I saw no downside. I grabbed my iPod, booted up iTunes, and downloaded the app. This is when I realized 3 things.

1. I have a first generation iTouch. It's running iOS 1.1.5;
2. If I want to run apps, I need to pay 5$ to upgrade to iOS 3.0.0 or later (since 2.0 isn't available).
3. Even if I upgrade my iTouch's OS, I don't have a wireless network, which means I can't use the authenticator app even if I could get it onto my iTouch.

So now I have the authenticator app in iTunes and no way to use it with my ancient brick of an iTouch.

Is there any way I can emulate an iPhone on my PC so that I can run this app?

Alternatively: is there any way I can emulate an Android device on my PC so I can run the android versoin of the app?

Yes, you can legally run an Android App.

You have to install the Android SDK, which can be downloaded here. Having installed it, you can create a virtual android phone on which you can install anything you want.

No. Not legally, nor technically.

1. The iOS simulator only runs in OS X, and thus on Mac hardware and
2. Even if you did have a mac and the simulator, the iOS simulator can only install apps if you have the package and install it through Xcode.

A comparable alternative solution would be to install a version of Android in Virtual box, which can be run on a PC and find a comparable Android application to install in the virtual android device.

Legally, no. The iOS SDK and included iOS simulator are only available for Mac OSX.

Someone has already mentioned the emulator in the Android SDK. A couple more Android-on-PC options:

You can run an x86 version of Android on a spare PC or on a virtual machine with virtualization software like VirtualBox or VMWare Player. This is a bit flaky as it's still relatively experimental, won't support Android apps with ARM code, and with the snapshots I've seen, if you want the Google Play Store, you need to shoehorn it in there yourself.

Bluestacks -- a sort of Android-on-Windows layer; It's an easy install, but it's pretty loaded with advertising. It can run apps like Google Drive that don't appear to be compatible with Android x86. The Google Play Store is on there, although you have to install a third party launcher (like ADW Launcher) to run it.