The Kindle Fire is a good choice, but you will have to root in (temporary rooting works, doesn't have to be permanent) to get Google Calendar on the device. It ships without that app and without the ability to sync to Google Calendar, that's why you have to root it.
It's sad, but I fear the PlayBook may be a dead end device. There are very few 3rd party apps and RIM has been slow to evolve the OS. For affordable 7" tablets, the Samsung Galaxy Tab 7 Plus and Lenovo IdeaPad A1 are also options. I'd pick the Tab 7 Plus but it does cost more. Both are reviewed on our site.