Getting a Schengen visa without firm travel plans

My girlfriend and I have South African passports with 5 year ancestral visas for the UK valid until 2018; we've been working here for a few months and have UK bank accounts. We're planning on saving up our earnings to tour around Europe in a few months. We don't know where exactly we'd like to go or for how long - just go where we want when we want.

A Schengen visa would be ideal as it would open a few countries to us. However two Schengen requirements may pose a problem:

1. We require tickets in and out of the Schengen zone (not much of a problem since we could get ferry/plane tickets from and to the UK a few weeks apart).
2. We require proof of hotel books or offers of accommodation from whoever we're staying with (this is the big issue as we don't know where we want to go).

Does anyone know whether not having firm travel plans would absolutely prevent us from being granted visas? Does it make a difference that we are UK residents (we have UK bank accounts and an address we can use but not Right of Residence or citizenship) or that we have leave to return to the UK after our Schengen visa would expire?

Surely you can go to the Schengen zone without knowing where we want to go or exactly where we want to be on a certain date; isn't that the point of a Schengen zone - one visa for all countries?