Day trips when staying in Oxford England

The obvious ones are Stratford-Upon-Avon or Warwick. You could also do the Cotswolds, but for that you really need a hire car. Only hire it on that one day though, driving in Oxford as a general thing is not a good idea.

Another obvious one is London (train to Paddington).

If you don't want to rent a car, this company and this company offer day trips into the Cotswolds, to Bath, to Stonehenge, and elsewhere nearby. Another tour of the Cotswolds starts in Moreton-on-Marsh, an easy train connection from Oxford.

We will be there in September also, and I posted a question about these companies on this forum but got no useful replies. We signed up with one of them for a Cotswold tour, and we also plan to take trains to Salisbury for a day, about two hours each way.

Another interesting trip would be to nearby Blenheim Palace, one of the largest of its kind and associated with the Churchills. There are guided day trips and also local bus connections you could use.

Here's a useful website for planning an Oxford visit, if you haven't come across it. With ten days, you'll have ample time to see what's in Oxford plus the surrounding area.

In addition to the previous suggestions, have you thought about Bletchley Park? We found it fascinating. Located just past Milton Keynes, I think it would be an easy day trip.

Here is one to include:>http://www.blenheimpalace.com

Blenheim - reachable by bus.

Just a few suggestions besides the great ones that have already been given...
If you're a Downton Abbey fan, Highclere Castle is not far from Oxford...about 25 minutes away. Even if you're not a fan it's a lovely country home with beautiful gardens to wander.
William Morris' house, Kelmscott Manor, is in the area.
I also really like Broughton Castle, about 40 minutes away.

Highclere has very limited opening times for the general public - do a search on the site for other threads on the subject if you are interested.