Where can I find vampires in Skyrim?
Broken Fang Cave, Bloodlet Throne, Cronvangr Cave, Fellglow Keep, Half-Moon Mill, Haemar's Shame, Mara's Eye Pond, Movarth's Lair, Pinemoon Cave, Shriekwind Bastion, Potema's Catacombs.
Source: UESP wiki, "Skyrim: Vampire" article
For PC users, the mod, DFB - Random Encounters can add various random encounters to the game, including Vampire encounters. You can configure the chance of encountering, difficulty and quantity of the Vampires that you can encounter with the mod.
Also, see this Gaming SE question and its answer(s): Is there any way to ensure you become a Vampire?
Does the DB Sanctuary really count for the purposes of the OP's question of wanting to contract Vampirism? The only vampire I'm aware of there is Babette, and as a child she doesn't participate in combat therefore wouldn't use Vampiric Drain allowing for the infection to be caught.
Easiest way to become a bloodsucker would be to join the Dark brotherhood. There is a target that is a vampire and your "brothers" will warn you that he is one before you go to kill him. Important is that you strip your char (take of your armor at least) and let him hit you while you are naked. You'll catch the "disease" easier that way. The Npc is called Hern.
I know of a few random places where vampires can be found as well: Pinemoon Cave, Morvath's Lair , Bloodlet Throne and Shriekwind Bastion
If you have "Dawnguard" then during the DLC you recruit three people and two of them continuously give you missions to go kill vampires, so if you want to be a vampire then you can just contract it from them.
P.S. To get these missions you must have completed at least two missions in the main "Dawnguard" quest line, but they are very easy.