Oxford and York bed and breakfast recommendations

In York I would recommend Abby Guest House B&B, especially if your arriving & leaving by train.
(It’s a five minute walk from the train)

We stayed at the Abbey Guest House several years ago for three nights and liked it. Right on the river bank, close to the station and RR museum, and a short walk to the center and Minster. They had limited free parking if that matters. I believe it has new owners now, so things might have changed.

Yes we stayed at Abbey Guest House (2017) too. You didn't say how you're getting there, but its a easy walk from the rail station, and they do have a small parking area behind if you're driving. Everything we saw in York was walkable from there.

Oxford:
I stayed at the Best Western Linton Lodge this past fall. It’s a hotel—not a B&B, but it has a great breakfast buffet and it’s in an Edwardian building. It’s in Summertown, so it’s a healthy walk into the centre or a bus ride (buses run often). Probably not what you’re seeking, but I had a good stay and can recommend.

The place I stayed in York was great, but the owners have retired.

Oxford - We like the Lakeside Guest House. It's right on the main road coming in from the south. It takes about 10 minutes to walk into central Oxford or you can catch the bus straight into the center, right outside the door. Very reasonable prices, incredibly clean, and a breakfast that is a cut above most B&Bs. Highly recommend!

York, the small hotel (with parking) that is near city walls is excellent:
The Minster Hotel York
60 Bootham
York
YO30 7BZ
GB
+4401924621267

In York last May we enjoyed our stay at No.21 York Bed and Breakfast. Our en suite room was comfortable, slippers and robes, friendly hosts and an extraordinary breakfast each day. Short walk from train station and short walk to sights. Safe travels.

Thank you to everyone for the helpful suggestions. Always best, I believe to ask for advice for making reservations. I will be following up with the suggestions recommended.

Lynette, looking forward to our trip

I can't make a personal recommendation yet but my mom and I are staying at this BnB in September:

https://www.airbnb.com/rooms/4930421

It has a lot of good reviews.

Sorry, meant to say that this is a BnB in Oxford.

Gillygate Guesthouse in York. Ideal location and Mark & Joyce are fantastic innkeepers.