The Park is located in Waimanalo near Makapu'u Beach, about an hour bus ride or 30 minutes if you have your own vehicle if coming from the touristy area that is Waikiki Beach. I would recommend, on a budget or not, to rather take the bus that regularly plies Kalakaua Avenue, the main thoroughfare that's steps away from the world-famous shoreline. For about $2.50, you get to enjoy the ride like a local and in the process sight-see other parts of the Island.
The cost of the tickets to the Park depends on whether it's the peak season or not. As we were there in the first week of January, we got ours for $169.99 each that included Park access, a $15 meal credit at the food court, and a dolphin fin shake and kiss. The latter was the culmination of my half-day visit to the park, and a photo is now in a fridge magnet and amongst others from my previous travels.
I never got to see the giant walrus that spewed vomitus at a zookeeper in one scene of the movie, but Penguins made several appearances for a photo opp. Also, don't miss the Penguin Cove Show, which proved to be a hit with the guests.