The highly anticipated iPad mini is expected out in a few hours. Aside from being a more portable and possibly (hopefully) cheaper tablet, I see various opportunities for a 7.8 tablet where a larger and more expensive iPad would be too big.
1) Onboard entertainment - A 7.8-inch iPad is about the size of most airline LCD screens but it can do so much more than playback video or music to keep airline, train or bus passengers entertained. With the advent of WiFi in the friendly skies, renting out iPad minis with access to games, email and social networking might make flying more bearable.
2) Point of sale systems- A number of establishments use iPads as POS systems and there are already a number of solutions that will work via WiFi so an iPad mini will be a cheaper and more mobile alternative for local, transaction based solutions.
3) Education - For courses that may not require a keyboard for input, a small iPad for each student could serve as a great tool for reading texts, taking tests and running education specific apps such as flash cards.
4) In-vehicle entertainment - I can see parents outfitting their minivans with various iPad minis behind headsets loaded with movies, music and games to keep various kids entertained during trips.
5) Kiosks - Quick surveys, electronic voting, promotional contests. All of these are ideal scenarios for using smaller tablets provided the tablets are well secured.
6) Advertising - The iPad mini would be powerful enough to serve ads in high-traffic areas like airports, washrooms, bars, waiting rooms and even trains. The devices can be used to play video, slideshow-type ads and even run questionnaires.
7) Security - it may be a costly option but with a FaceTime camera, the iPad mini would be an ideal security access control system to capture images or faces of guests while managing entry or buzzer codes.