The 'semi-official' bf cafe is The Magic Cafe on Magdalen Road? - not quite central but not far off.
Borders is NOT very comfortable in my experience - I did do it, but it was extremely brightly lit and it seemed hard to get the right support in the chairs. Also a lot of coming and going. Best if you can tuck yourself just beside the screen that is between the 'thoroughfare' by the door, and the main bit of the cafe. At least you can lean on the screen then.
There is a lift up AND down to the Modern Art cafe, and although it takes ages, once you are there it's a serious good'un and feels quite spacious for Oxford. Having said that, most of their 'comfy' chairs are a bit supportless tbh.
What's that cafe in the middle of the Covered Market that has a sofa and chair in it? I think of it as Georginas or Brothers ,can't remember which? If you get into town really early (which I always used to do, wondering where all the other 5am wakers were) I found that comfy and relaxed.
BHS canteen is not bad at all (first floor, like every other place in Oxford). Ditto Debenhams canteen, although their baby change is DIRE DIRE DIRE - there are two separate bits of room with heavy doors down a corridor. The first time you go, try and check it out without the pushchair if you can. Is your ds young enough to be in a sling? If so, take advantage!
Because everywhere in central Oxford puts their children's stuff on the first floor, people on the ground floor tend to be quite helpful about secreting your pushchair there for you to pick up later. This is an option at Modern Art too.
Boots first floor is quite nice - haven't checked out the actual facilities though. And handy for spare nappies etc.
will keep thinking...