Just something to note, the DSi "specific" software (the downloadable apps/games etc) are region locked so you won't be able to play them here on a U.S. DSi.
Normal DS games aren't though so if you're intending to just buy the physical cart based games, you should be fine.
"DSi software (software that is only compatible with DSi) is region locked, eg: European DSi software can only be played on European DSi consoles," a Nintendo spokesperson has told CVG.
They confirmed that this means BOTH download-able games and future DSi-only cartridge-based games would be region locked.
"Nintendo DS software however is region free so you can play any DS software on DSi from any region. You can also browse the Internet on your DSi wherever you are in the world and exchange your photos with friends from around the world."