The Plain is being rebuilt and ambitious plans to redesign St Giles have been floated, but for me the most obvious redevelopment for central Oxford, the one that will cost the least and deliver the most, is Broad St. All that is basically needed is to remove the car parking, remove the kerbs and resurface the entire area, drop the speed limit to 5mph and perhaps time-restrict access, and Oxford could have a showpiece central square.
Broad St is a fantastic space, with the frontages of the Sheldonian, the Clarendon building, the old Oriental Institute, Trinity and Balliol colleges, and so forth. It is already a kind of bike parking hub and a tourist centre — it has the biggest tourist information centre and seems to be where tour groups assemble — and is already used for occasional markets (though they are always crammed into a small space at the western end where they block a major through route for pedestrians and cyclists). Broad St should be a grand square, the very centre of Oxford, where people meet and eat and drink and wander. (The other candidate for this is St Giles, but that carries one of Oxford's major through routes so would be much harder to reengineer.) It's never quite going to be a Piazza San Marco (Venice's biggest square and tourist centre) but Broad St has the potential to approach that on a smaller scale. It's simply madness that a space with this potential is used as a car park and motor vehicle turning area, with only narrow pavements for the throngs of students and tourists and everyone else.
The first, and biggest and hardest step, would be to get rid of all the parking. After that everything would follow fairly obviously. The remaining traffic — deliveries and loading access (perhaps time restricted), maybe some disabled parking, maybe Queen-St-speed tour buses — would be sufficiently low volume that the space could be used as a square rather than a road. That is, pedestrians and cyclists would freely use the entire space. The obvious followup, to make the status of the space clearer, to make use by pedestrians and cyclists easier, and to make the space more attractive, would be to remove the kerbs and resurface the entire area to make a unified space. Throw in some new signage on the Parks Rd entry ("do not even think about trying to park past this point") and that's pretty much it. (Hollywell and Catte Sts and southern Parks Rd could be reworked as part of this redevelopment, but that's not essential.)
Doing all of this nicely will cost a bit, and abolishing the parking will take a bit of political will, but compared to the costs of rebuilding St Giles (even without a new tram line) it seems likely to be relatively cheap, and the engineering is certainly more straightforward. The potential gains — for central Oxford as a place to visit, shop, walk, and live — seem huge.
Update: Nearly Car Free is I think a better term, both for New Inn Hall St and what I propose for Broad St.
Update: Thinking about this some more, and taking comments on board, I still think a square with general pedestrian freedom is the right goal, but that bicycle paths should be marked/set out down the middle, connecting to George St, with a side-branch to Turl St. That would provide routes for cyclists going through Broad St at higher speed, which pedestrians could cross but where it was clear they shouldn't be lingering. (It would also provide routes for motor vehicles when access was needed for loading, etc.)
The Oxford Preservation Trust has had a Plan for Broad Street since 2004, most of which remains perfectly current, but there are no signs they had any luck getting it adopted.