Yes. [resists the urge to say the center of the cryodiil zone]. Err there are 6 special spawns found in the high level zones 2 to an alliance around the game. They only spawn during the dark of the moon. Only those specific NPC spawns can infect you.
You can also try to talk another vampire player into infecting you but they can only do it once every 7 days.
Are vampires in the game yet? If so where do you go to get infected? Do I need to be a certain level to get infected? Thanks!
You get infected at specific spots and times in high level zones, by bloodfiends.
The guy who did the tutorial on here was level 20 at the time, but the mobs he was fighting were 40s. So practically, you probably will not be able to do it at least till your 20s. And you will need to complete the quest to actually become a vampire.
Vampires have been in the game since beta and were there at launch. There are severe drawbacks to becoming one, so most people will only do it for RP purposes. It is probably not going to give you a net advantage in-game as far as PvE or PvP.