I'm travelling with a couple of friends and their 2-year-old in July. We'll be in Oxford for most of the time, while one of my friends attends a symposium, but then have a few days afterwards before heading back to the States. Looking for suggestions for child-friendly day-trip options around Oxford, as well as something easy/interesting to do those last several days.
You can't go wrong in London - even with a toddler. The amount of green-space is just incredible and the whole of the city seems 'kid friendly."
If you go to London, I would recommend the public buses over the tube. Not all tube stations are "accessible" and I'm sure you'll be using a stroller/pram at times. Also, the buses are much more "stroller" friending than the tube carriages.
In addition to miles of walking paths and the Princess Diana Memorial Fountain, Hyde Park also has the Princess Diana Memorial Playground.
Other ideas in London include the Zoo, the Aquarium, and Kew Gardens.
From Oxford, you can be at London Paddington (for Hyde Park) or Marylebone (for the Zoo) in about an hour with not train changes.
I will "second" the idea of London. We were in London for a week last May with my son's family, including grandchildren aged 22 months and 4 years. The toddler particularly enjoyed Kew Gardens, where a peacock put on quite a display, and the Thames path on the South Bank at the eastern end, around Shad Thames and the London City Hall. There is a broad open space with nautical structures that invite climbing, and a water feature (fountain and a little stream) that kept both children happy for an hour, floating their Croc sandals and chasing them. The photos from there, with the Tower Bridge in the background, are priceless.
Hyde Park, accessible from Paddington with a short walk, is also a good idea. In addition to the playground me tinned above, there are some museums of interest to children across the park on the south side. The Natural History Museum had a butterfly garden when we were there, and both kids loved that. The Victoria and Albert has a central courtyard with wading pool and outdoor cafe---a good spot for lunch.
As noted above, the buses are very stroller-friendly. You would need a one-day Travelcard or Oyster card to use them, as the drivers no longer sell tickets on board.
Stonehenge is about an hour and 45 minutes away. Some folks can't understand all the fuss. I'm of mind "how in the world did the move and stand those rocks?" Not to mention will we ever definitely know why it's there? Its purpose?
I too say consider London. So much to experience there. How about some mudlarking? A Jack the Ripper tour? A duck boat tour on the Thames? Paddle boats at Regent's Park? An outdoor performance at Regent's Park outdoor theatre? A walk along the canals of Mida Vale? Portobello Road, Camden Lock, Brick Lane, Spitafields, Brixton markets? Mudchute farm? Not to mention meandering around Parliament Square. Seeing St James Park. Hyde Park. ( Ducks at the Round Pond) Regents Park and the London Zoo.. Kew Gardens.
Lastly, if any one in your group loves geology and dinosaurs you could visit Lyme Regis and the Jurassic Coast.
Personally, I would figure out what you want to see and make it a kid friendly experience.
Example: go to Blenheim Palace. Two year old will love to run around the gardens. They can do that for an hour then they might snack. Probably 20 minutes of indoor look at this, don't touch then they need to run or eat. With enough exercise, they might nap. Bring a stroller or backpack (if allowed). Continue with your tour. Split up as necessary. Always have food and Drink on hand. I'd bring those pouches of applesauce, too. Great for travel.
I find that travelling with a little kid involves doing what I would normally do but in a different location: feed kid, exercise kid, let kid nap. Or doing extraordinary stuff in small doses so kid doesn't flip out. I guess that works for bigger people, too!
Check out KidZania for role play - not THAT kind of role play.
Check what people in Oxford do with their two year olds while you're there. Is there a circus on, a fair, a kids concert, a kids show? These are not just for locals.