We will be arriving in Orlando at 2pm. in the afternoon. We purchased a special package that will only begin the next day. Are there any parks that offer 1/2 passes?

There is plenty to see at Downtown Disney (shops and restaurants). This area doesn't require admission and would be a nice way to start your vacation before hitting the parks.
I would highly recommend dinner at Rainforest Cafe at Downtown Disney for your first evening. Good food and entertaining too Be aware, though, that the wait can be very long to eat there if it's a busy time, so get on the list early.
~Katie

Since you probably won't be at your hotel and checked until until at least 4 (and therefore couldn't possibly be to a park until 5), I'd suggest something else. Try one of the expansive miniature golf courses at WDW, or if you are staying closer to Universal, go to CityWalk and enjoy the area and a movie. Then get up early the next morning to visit the park of your choice. Flying all day is tiring, especially for kids if they have to get up early, and I think you might get more out of the trip if you don't try to do too much on day 1.

I know if you buy a single-day ticket for Sea World, you can return free the next day regardless of when you arrive at the park on Day 1, but no half-price deal as far as I know. In the past the arrive after 3 get the second day free thing was common, but never a reduced price ticket. Other parks may be offering similar deals right now. It's also cheaper at Sea World if you buy tickets online in advance.

I agree that there are many ways to spend time in Orlando without purchasing a park pass. Downtown Disney is full of restaurants and shops. There is a Cirque du Soliel there. The Disney hotels have very nice restaurants with some offering views of the fireworks over the Magic Kingdom. There is also the Boardwalk area near Epcot that has various shops, restaurants and street performers. CityWalk at Universal also offers the same.

Our favorite ways of spending the first afternoon in Orlando include bike or surrey rentals, golf, swimming at the pool etc.

Check out disboards.com and allearsnet.com for more suggestions.

We have gone to Disney more times than I would like to admit and our arrival day activity is always Downtown Disney. It really helps us get into a Disney mood.

Ditto the rec's for Downtown Disney. What hotel are you staying at? If you're going with kids and staying on-site, they may be happy just to hang out at the hotel pool. (Or venture over to another hotel's pool -- the Caribbean Beach Resort just opened a new pool area.)

Thank you everyone...Downtown Disney it is! I appreciate your help.