Unless you are planning to do other things in the West Palm area, I would say it is not worth the day trip. I used to live in west palm and have been a couple times, but it is out of the way for a day trip. I would recommend Cape Canaveral or Dahli museum in the Tampa area for a day trip. Each are about or under an hours drive.
we live here in plam beach county and it is WORTH it! we have season passes now due too all the improvements. let me tell you its like animal kingdom there. granted the lions are not free to come right up to your car for safety reasons but everything else just about does! there is a great waterpark area, ferris wheel, cute baby giraffee feeding area. there is alot to do. you can bring in lunch without a issue and have a picnic. It truly is one of our kids favorite places to visit!
I've never been, but I think someone made a good point, that will be 6hrs round trip. We've done the "lion safari's" elsewhere. While they've all been cute, I don't think any were 6 hrs cute.
We haven't been in a few years... since they made the improvements. But now you all have me wanting to take the kids! I think we'll wait until school is back in and it gets a little cooler though.
For a 6 hour round trip drive... I don't think it would be worth it if you are already experiancing Animal Kingdom. If you are looking for day trips, maybe Tampa for Busch Gardens?