I am interested in developing an app for my new iPad purely for my own use. (well to start with at least)
You can develop for iOS without a Mac by using Adobe Flex. The Flex SDK is free and Open Source, and includes a compiler + packager. If you want an IDE, you can get Adobe FlashBuilder (not free, but with a free 90-day trial), which makes your development time much more productive. You would not develop in C, C++, or Objective C, but in a combination of ActionScript (a dialect of Javascript) and MXML (markup language, mainly for rich GUI layout).
On the minus side: you have less control over what you can do (you can still do a lot) and you cannot use the iOS SDK directly.
On the plus side: it is very easy to develop great looking apps, and with very little changes, you can recompile them for Android, Blackberry Playbook, Windows, and Mac OS X.