When I travel, I love to walk. Wandering around is, by far, the best way to get a feel for a new city. Just imagine peering into alleyways for hidden shops, stopping for a coffee and a chat with the barista, and really discovering all the things you'd whiz by if you were in a cab. Needless to say, I'm stoked about downloadable walking-tour apps.
Here's how they work: You visit the site (Walki Talki and GPSmyCity.com are two big names; iTunes has a ton as well), and download the particular tour, whether it's a general-interest jaunt around Paris or one organized by a specific theme, like architecture in Barcelona. Typically, the apps include narrated and/or written info on major sites, directions that you'll follow from spot to spot, and a map (Walki Talki has one you print off; but with GPSmyCity.com, the map is on your phone). Because you download everything before you head out, you don't have to worry about establishing Internet connection or racking up insane roaming fees.
Side note: Before you download, check out the tourism board's website for your honeymoon destination, because some cities, like Buenos Aires, have audio tours you can download for free.