I used to live in Oxford. The Oxford Story Museum in Broad Street is a must with children, www.storymuseum.org.uk/
Similarly, Oxford Castle www.oxfordcastleunlocked.co.uk/ with a mound you can climb, a tour of the former prison and a bit of open space to run around in.
The University Museum of Natural History in Parks Road is stunning, full of dinosaurs, fossils, shrunken heads (in the Pitt Rivers at the back) and much, much more.
Pick up a tourist map and you will find a peaceful canal walk close to the bus station. You can walk all the way to ancient Port Meadow if you're keen.
From St Aldates it's a short walk down to Christchurch College, beautiful quad and Oxford Cathedral and just beyond, Christchurch Meadows, gorgeous walk in spring especially and will take you all the way to the river. You can take a boat trip to nearby Abingdon and back.
I can recommend the Tree Hotel in Iffley Village. You'd have to check the prices or look on booking.com but it's very pretty there and is a short bus ride into the centre or a wonderful walk beside the Thames from Iffley Lock. The University usually only has rooms in the vacations and nowadays not even then but it's worth a try.
Hope that helps.