Check out the Durham if you want to catch up on Omaha history. Lauren and I have ben here a few times and it is pretty cool.
Omaha's zoo is pretty great, and a pretty big attraction for the city. I can't say I've ever been in the winter, but it is still open so I'm sure it'll be cool.
The Old Market is in downtown Omaha and has a bunch of bars, restaurants and shops. It should have a bunch of Christmas lights too. Try to check out the enclosed alley - look up Trinis Mexican Restaurant and you'll find it.
Jake's Recommendations:
Cunningham's Pub and Grill
One of my favorite places to eat in Omaha. The food is great and I love the atmosphere. This is closer to the wedding reception area.
The Crescent Moon
This is a cool bar and grill in Midtown. Its has made my list for "Top 3 Reuben Sandwiches in Omaha". You can get a boot of beer downstairs at the German bar too.
Buck's Bar and Grill
This place is outside Omaha in Venice, Nebraska. It is one of my favorite places because it pulls in some great country music artists for concerts. Its such a small place, but that is what makes it cool. You have to sneak past the guitar player to get to the bathroom. I'm putting it on the list because I love this place. Check if there is a concert while you're in town. Please don't skip our wedding for it though.
Breweries
Omaha has some pretty solid ones. My favorites are Lucky Bucket and Nebraska Brewing Company.