Well I have been asking around this a variant of this question to some of my good friends in real life and one told me that the best for Archer Assassin is the Dark Elf. The other favors the animals for everything (Khajiit and Argonian). But my current and favorite is Wood Elf. Now I am aware that under the bio of wood elf it says that they are the best archers un all of Tamriel but I didn't know if that was just for role play or it is really their stats. Now me being a LoTR fan I had to pick a Wood Elf for Archer Assassin. What do you guys think?
Aside from racial bonuses all races are the same, the wood elves start with +10 archery skill, but any race can be an archer, it just means that they will start 10 or 5 points less, which is probably about 30-40 minutes of bow combat at low level.
If you were going to pick wood elf that just means it's easier for you to begin with because you start with stronger bow damage.
In truth any race can be as good an archer as any other, if anything perhaps khajiits night eye power is most useful for an archer to get an easy shot, but then again any player can become a vampire which gives them the unlimited use of night eye as well, so you can see in the dark as much as you want with any race.
In short all races end up equal in regards to archery but wood elves start with more skill in it.