Ooh Strangeways this is my home turf! I would recommend Chiang Mai on the High Street. Some call it the best restaurant in Oxford. It's down a little alley (but very central) and in an atmospheric Elizabethan building. The food is much much better than at Old Tom's (sorry to the previous poster!). And they take bookings. A favourite haunt for locals entertaining visiting academics.
I also LOVE the Cowley Road. My two favourite local pubs are the Rusty Bicycle on Magdalen Road (delicious burgers, maybe the best in Oxford), but they are often crowded on a Sunday night, and I don't think they take reservations unless it's for a party of 4. That said they do have outside seating with heaters. A much-loved local hangout.
The Chester pub (which is not far from the Cowley Road, but off the Iffley Road) is also legendary. Their steak platter is to die for. I'm not sure they take reservations either though!
Apart from the Rusty and the Chester, my family's favourite two Cowley Road restaurants are Le Kesh (Lebanese/Morroccan cuisine, delicious chicken shawarma and tagines) and Taberu for Japanese (top quality and not too expensive). However, you didn't mention those cuisines I know.
My two DS love all these places.
DM me if you have any questions! And enjoy!