I've had my 3DS for a year now, but I haven't really bought anything for it yet.
get the battery pack
adds 10 hours of battery life
Not all that useful if you don't play for more than 5 hours a day and recharge every night. My 3DS is on all day (because I just love StreetPass!) and I can put in a good 5-6 hours of gaming (usually DS-games) before it needs a recharge.
What I would get is some form of protection if you plan on taking it with you. Mine lives in a a DSi sock I got for free once, but there are better (and fancier) options.
As for things to do: start playing StreetPass! It's loads of fun, especially if you live/work in an urban area and lots of people walk by every day. You see, once you've enabled StreetPass, and your 3DS 'meets' another 3DS, the Mii in that 3DS will visit your 3DS. It happens automatically while your 3DS sits safely in your bag. The two main StreetPass games are really simple, but very addicting. One is collecting puzzles, the other one is kind of like a reverse tower defense game with RPG elements.
And keep the game suggestions coming.... I'm compiling a list that seems endless at the moment! AND I'm SUPER EXCITED TO PUT A CHECK AFTER EVERY FREAKIN' ONE I HUNT DOWN!!!! hahahaha
You like your games cute, right? How do you feel about the Atelier series? There's one for the DS called Atelier Annie.