H.D.
Hi-
I have a 13 month old who also likes to go outside! We live in Wauwatosa- a nearby suburb. One great option is to get a zoopass. The Milwaukee Zoo should be around a 15 min drive and a great place to run around (they do have a playground in there too). It is about $55 without parking for a year pass or $87 with parking.
Otherwise, all parks are about the same here. We've gone to one on North Ave but typically go to the ones in Tosa. The one outside of the Waukesha library is pretty nice but probably too far for you. There are tons of hiking and biking trails in WI but probably not as appropriate for a two year old (look up ice age trail)
Good luck finding places in Brookfield! We also go to Gymboree (Ruby Isle plaza). They have open gym three times a week- free for people taking a class and $5 for those who aren't.
Good luck!
H.