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Grays Farm PYO over near Wokingham - not exactly cheap as you spend money on the food you pick. Thought I'd mention it here though, just as another place to go, as I remember places I've been to in the past.
Car parking is £1.50 for four hours at Dinton Pastures. South Hill Park in Bracknell always has ducks, and they are just renovating the play area. Free Parking. Also Jocks Lane and The Pavillion in Bracknell are free parking, playparks and outdoor paddling pools, all free. The Play rangers are visiting these parks throughout the holidays and providing extra activities on certain dates, ie bouncy castle, rock climbing wall also all free. Henley has a lovely "Wind in the Willows," museum although don't know what the charges are. Hope this helps.
Now I've taken two non-swimming children swimming not sure about taking three... that might be a bit much. Thanks for the suggestion, when I have just the two under 5's during school-term time we do go swimming at Coral Reef.
Have invested in an annual pass for The Lookout. Have had one before and we went loads. On a wet day like today it's great as the children (all 3 of them) will be happy for around 5 to 6 hours there. Even baby was happy to splash around with the boats and crawl about getting in the way of people
Are any local museums any good? The Museum of Reading is ok, though train fare keeps going up.
You're not too far from Basingstoke canal if you all have bikes it's a nice cycle ride (maybe a picnic). I don't think you're all that far away from the Alice Holt forest in Farnham (only have to pay parking), also very good for cycling (you can hire bikes if you don't have) but even nice for exploring by foot (adventure playground etc...). Sorry I don't know Bracknell at all, but these two places are only a short drive and virtually free.