I've researched this extensively and the only other place near Orlando besides Discovery Cove is in St. Augustine (about 1 hour north of Orlando). I think the place is called Marineland.
Other than that, there are a couple of places in the Key West area. The one closest to Orlando (but still probably a 4-5 hour drive) is in Key Largo. It's a place called Dolphins Plus.
Since we are going back to Florida this year for vacation (but not visiting Disney or Universal...time to do something a little different) and will be visiting Busch Gardens instead, we decided to take a side trip to Key Largo to do some snorkeling and to swim with the dolphins.
By the way, Dolphins Plus charges $160 per person for a structured dolphin swim. I think it's about 45 minutes actually in the water with the dolphins. If I remember correctly, Discovery Cove is much more expensive.
Hope this is helpful.