Don't mind travelling a bit, just want a few ideas for a different day out with a 6 year old and a 3 year old. Ideally not to expensive as we have a few expensive trips etc planned already! We're near Southampton but don't mind travelling for something a bit different
I go to Wellington Park near Basingstoke - it's good for younger children not sure older children would enjoy it as much although there are some climbing frames and a zip wire in one of the playgrounds.
Also yesterday I went to Millets Farm Centre. It's just south of Oxford - only an hour from north Hampshire, probably less if you went straight up the A34 It has an amazing falconry centre which even my 2yo sat through the display, some animals, nice cafe/restaurant, very small playground. Might be worth a trip, if it's a wasted trip at least there's a nice farm shop and ice cream stall!
On a good weather day, you might like Furzey Gardens or Hillier Gardens. If you are Nat'l Trust there's Mottisfont and other sites in the area. Also, a day out in a different town/village can be fun. So you might like to explore Romsey or Winchester.
Marwell Zoo is also an idea but more expensive.
If you like swimming, you might like the indoor water park at Romsey Rapids but be warned, children are shattered by this so plan carefully in relation to naps and plan lots of snacks/picnic for before and after.