There's so much to see in Oxford, just wansdering about. Look out for the Gormley statue on top of Blackwells Art shop on Broad Street!
Thirsty Meeples Games Cafe on Gloucester Green for fun and Cafe food.
If you're going to Pitt Rivers, the South Parks is right next door if you need a run around!
Worcester College has massive gardens, and Magdalen has the deer park. Botanic Gardens also lovely.
Punting is a possibility if the weathers nice, but I've never seen life jackets for youngsters. Magdalen Bridge.
There are lovely half hour boat trips from
Folly Bridge, book in advance https://www.oxfordrivercruises.com/sightseeing-highlights-tour/?gclid=CjwKCAjwpKveBRAwEiwAo4Pqm6OcUeZOxJX3mSy2BDeTSRnTlwMUvvu-gAHfCZEBU54-ka-FYAMdxoCaWkQAvDD_BwE
You need tickets for the Tolkien exhibition at the Weston (its small and not really great for children, either)
Opposite Christchurch is a lovely Alice in Wonderland gift shop which is worth a pop-in.
The Covered Market is not that interesting for children, but there are some nice shops and loads of cafes.
So many places to eat, but I find the new Westgate soulless and bland. There are all the usual chains like LEON, Bella Italia, Pizza Express, but I'd avoid and take advantage of the so many independent places in town.
Handlebar Cafe, the Nosebag, Crisis Cafe, any of the G&Ds, the Vaults Cafe at St Mary's. I'm not sure about 'posh' places to eat as I rarely use them, but the Randolph and No 1 Ship Street are recommended.
Oxford Castle (up past the Westgate) www.oxfordcastleandprison.co.uk/
There are places to eat there.
Hope that helps