If you're dead set on going to Stonehenge, Salisbury would be a better base. It's not a bad place to spend a day either, nice cathedral and old town centre and the local bus company runs a handy tour from Salisbury if you're on public transport. Oxford is worth a visit, and I would personally go to Bath rather than Bristol as a tourist (not to live, mind). By the same token although there are interesting things to see in both, as a first-time visitor I probably wouldn't choose to visit Birmingham and actually probably not Manchester either, unless seeing post-industrial Britain is part of the point.
Also be careful not to spend all of your time running around catching trains, and don't give yourself too many connections to make - the British rail network is almost as unreliable as it is reputed to be.
If you land in Oxford last in the South then there's a handy crosscountry train service direct to York that isn't too expensive.
Personally not a massive fan of Stratford-upon-Avon, unless you're a big Shakespeare fan obviously!
My itinerary in England with your time and requirements would like something like this:
Days 1-4 London
Days 5 & 6 Salisbury and Stonehenge
Day 7 & 8 Bath
Day 9 have a look at the cotswolds or some other countryside, or Bristol if you're dead set on it
Days 10 & 11 Oxford
Days 12-15 York
[ Edit: Edited on 21-Jul-2011, at 10:55 by magykal1 ]