Hi Mike,
I'm afraid I know nothing about football (of any sort) or much about local bands as I don't get out much these days. However, I do know a fair bit about twins as I have a set myself!
I highly recommend connecting with Canberra and Region Multiple Birth Association, who have quite an active social group. It's a good way to meet people and there are always people moving to and from Canberra. I'll PM you with some details. Alternatively MeetUp is another good way to find groups of people with similar interests.
Playgrounds:
Lots of playgrounds in most of the local and district parks, but be aware that nearly all Canberra playgrounds are not fenced and in the case of the district parks, tend to be near large bodies of water. The newest playground however is fully fenced and is called Boundless http://www.boundlesscanberra.org.au/. I haven't been myself yet but it is very popular from what I've heard and has been a great community project. It is near the Carillion, opposite Russell, parking is limited but you can park at Russell and walk across the bridge to the park.
Google will give you articles and reviews about Canberra playgrounds, for example
http://www.canberratimes.com.au/act-news/playgrounds-lure-little-superheroes-20130714-2pyez.html
Softplay:
I'd probably recommend Lollipops at Majura Park for the indoor softplay, solely because they offer a discount to multiple birth families so you will find it cost effective. There is also....
Kid City at Mitchell
Lets Play at Nicholls
Monkey Mania at DFO
I highly rate "Play Up", which is the permanent exhibition at the Museum of Modern Democracy...you can enter for a gold coin donation pretty much. Suitable for children your age as plenty of building blocks and drawing etc. It's excellent!
http://moadoph.gov.au/exhibitions/play-up/
Canberra is a great place for young families and small children.
Cheers
Janet