Hi Vikki
Our family (me, my wife and our two boys aged 4 and 7) arrived from the UK just before Christmas and we're using Rhodes as a stop-off for a few months, while we investigate other places to live.
We're on Shoreline Drive and there are three nice little parks nearby. One has a sandpit, which our 4 year old loves. Two have swings and they all have slides toddlers seem to use with a little help! There's also a play school just around the corner, but we haven't been: http://rhodescentralpreschool.com.au
Taking our boys to the Olympic park this Saturday for the free open air cinema. (The Croods is on at 8pm, perhaps too late for your little guy?)
Then on Sunday we're going to get Family Fun Day tickets. They only cost $2.50 each and you can go almost anywhere: http://www.sydneytrains.info/tickets/which/funday
Last week we went from Rhodes to Manly beach, via train and ferry, giving us a great view of the Opera House and bridge on the way.
My wife is working here as a midwife and I'm taking a career break for a bit, until we get the boys back into school. It can be tricky keeping them occupied all day, but at least there's no snow or flooding to cope with!
Hope you're settling in okay.