Don't forget your V5... but you can get quite far: the Russian border is about the limit really. You can buy a visa at the Turkish border (and Armenia too I think), you don't need one for Georgia. Any further requires a bit of pre-planning with regards to visa applications and even Carnet's for some countries. None of the Baltics or Balkans require a visa. Likewise, I don't think you need a visa for Morocco. This is all assuming you're a British passport holder.
When and where are you roughly thinking?
Georgia is gorgeous, it's about the furthest and you get to go through loads of other nice places to get there. If that's a bit far, maybe down through Italy across the Med and up through the Balkans (or vice versa), the Adriatic Coastal road is fantastic, very scenic and twisty, and Croatia is beautiful. It's probably getting too cold for a loop north through Scandinavia but I can reccomend Latvia, surprisingly nice.
South will be warmer of course, so I'd go to Morocco, plenty of adventure bang for your buck I reckon... mighty different to Blighty and Europe. Weather's still good, you can get a good taste of Africa and the Islamic culture/tradition, plenty of off road opportunities if that's your thing (rentals), cheap???... it just has lots to offer, at least that's what I would choose for a spontaneous end of season jaunt.