Ah, arthurian legends.
That is one of the reasons for suggesting Winchester. It is home to one of the (disputed) contenders for the Round Table.
The other reason for the recommendation is that Winchester Cathedral remains one of the great beauties in England.
Not in the west, but I would see if St. Albans (Verulaneum) is practical during your visit. It has one of the most complete amphitheatres dating to Roman times.
Back in the West Bristol is a high recommendation, (though if you have been to Bath you likely passed through there I guess). The Clifton Bridge is a tourist haunt. The Clifton Suspension Bridge is also where failing students at the University of Bristol fling themselves to their deaths. Most do not realize till too late that they will likely land feet first in the mud - there to die slowly from internal injuries.
Furthest West you would come to the beautiful countryside of Devon or Cornwall. If your visit is at the right time of year indulge in the scrumpy, a raw highly alcoholic cider. At pretty much any time of year Devon and Cornwall are great for an afternoon tea with scones, double clotted cream, strawberries and fruit spreads.
In Cornwall you will have to visit Tintagel - which is the past home of the English King believed by many to be the true King Arthur.
LINK
Not much is left of the castle -
Oh yes, for safe punting - here is a map that details the confluence of the Thames (its known as the Isis in Oxford don't you know) and the Cherwell, you can highlight the "danger" points, pubs and other data on the rivers.
LINK
Use the arrow up icon to move the map focus to the Cherwell.
Last,if you are a fan of weird but wonderful stuff, you could do worse than trecking over to Portmeiron. It is a model village built in the style of the Mediterranean, but located in Wales. Among its other claims to fame Portmeiron was the location on which the cult TV series "The Prisoner" was filmed.