I think Winchester would probably the best in terms of age appropriate things as well as nice hotels.
Activities Marwell Wildlife Zoo is about 7 miles away and has lots of different things to do - obviously the animals to see! But also has a couple of adventure playgrounds inside and a land train which my DSs really like!
If the weather is crap then there is quite a good soft play about 8 miles away called The Adventure Barn which has a good inside soft play area but also some outdoor activities.
InTech is a science/discovery centre about 3 miles away which has some good stuff for pre-schoolers if I remember rightly. It has lots of hands on stuff and a really cool planetarium!
Winnall Moors is a nature reserve near to the town centre which is quite interesting to play I-spy in! Although there is a river running through it so may cause more stress than fun!
If either (or both) of your DC likes trains then there is the Watercress line which is a ten mile steam railway that starts about 7 miles away. My DS who loves trains absolutely loved the whole experience!
Then of course there is always the New Forest National Park not too far away - there is a really good wildlife park about 15 miles from Winchester which isn't massive but is much better structured than some of the other parts of the national park on my experience.
I'm less able to help hotels wise (we lived in Winchester for a couple of years!) but I've heard good things about the Holiday Inn - but it's not that near the town centre.
If more countryside then the New Forest isn't too bad travelling wise and rural Oxfordshire is lovely. If you want to see the sea then the Jurassic coast is amazing and the Kent coast is very nice too.
Our weekend plans have fallen through. For 'big birthday' reasons we would really like to go away for a nice - not necessarily expensive! - weekend away. Is there anywhere we could do this, striking distance of London, with two under 4s?