Back when it might have been an option and you could quite happily play some NES games on your GBA, today there are so many better ways, ones that may even end up cheaper, to play NES games on the go. The main reason you want to avoid the GBA is because it has a lower resolution screen than the NES. Various things were done to dodge this (mainly pan and scan and tile trimming) but none are ideal. Other options include get a PSP (good choice really, if a bit basic), get one of the open handhelds (GP, pandora....) as most will tend to have a good NES emulator, get an android device and stick an emulator on it (worth it) or even a DS and a DS flash cart (nesDS and other things are better than the GBA had). Look hard enough and you can probably even find a device with a GBA or GBA sp style form factor if that is something you decide you care for.
Still
There are two NES emulators worth speaking of for the GBA
Pocketnes.
The main one people know of, even used in a few commercial games.
http://www.dwedit.org/dwedit_board/viewtopic.php?id=409 has some
http://nes.pocketheaven.com/ is the original.
You may also like
http://kuwanger.net/gba/pocketnes/
HVCA.
Its main claim to fame was it has more mappers than pocketnes (though pocketnes is no slouch and most of the extras are not common ones), better FDS support and a different scaling method (recall the resolution thing) that worked better for some games. I consider it pocketnes' equal in many ways.
http://wiki.pocketheaven.com/index.php?title=Hvca
Means to run it. The GBA needs a flash cart. The best still available is the EZ4, if you only want to run NES then you might also consider the EZ 3 in 1 as it might be a tiny bit cheaper (you will need a DS and DS flash cart to set it up), the option for a supercard is there and for the most part they run emulators but I do not like suggesting them even then.