Hi C.,
Depends on where you are within 33325. I'm in 33326 (Cooper City) but willing to go to Plantation, Sunrise and Davie, without hesitation. Volunteer Park is nice but they have separate toddler and older kid playgrounds. One of our favorites is a Sunrise park, Flamingo Park, just west of Flamingo Road on 8th street (between Broward and Cleary). It is shaded and all new equipment.
Other favorites of my 2 year old, Central Park in Plantation (just east of Nob Hill on Broward Blvd). Has swimming pool, toddler playgrounds (two), soccer fields, basketball courts, tennis, etc.
Jim Ward Sprinkler Park in Plantation (off of Broward, just west of 441). This is a FREE water park (no pools, just sprinklers) and I haven't found anything else like it, great for summer days.
Weston has a lot of nice parks as does SW Sunrise, check with the city websites.
Oh, and there is a very active Davie MOMS club for Western Davie if you are interested.
Best wishes, C.