To reduce the cost of days out, always take food and drink with you where possible. The cost 'out' is almost always extortionate for poor quality food.
If there are local attractions that you like that do annual passes, this can be a good way of accessing cheap days out because you pay once to go as often as you like.
For days out that you have to pay entry for etc, always look for vouchers etc. There is almost always a 2 for 1, kids go free type of deal available, or even booking online can save compared with paying the full price on the day.
English Heritage or National Trust passes can be excellent value if you like those sorts of places and have them nearby. Some employers, especially the public sector, offer corporate membership at a discount - see what benefits you can get through work.
Days out with DC, a holiday, and spending money for adults all has to come out of what's left after your essential expenditure. So it's also worth seeing if you can maximise your income in any way or cut your essential expenditure as both of these will contribute to making the pot leftover for fun stuff as big as possible.
For a complete and systematic way to overhaul your budget, have a look at:
www.moneysavingexpert.com/family/money-help/
Even if you don't spend more than you earn, cutting back on boring things leaves more money for fun things, so always worth doing.