Ah a fellow Malkavian! Pleased to meet you... and your large pink elephantine friend.

Malkavians generally centre around their personal dementia so any development should stem from that. My character had a sock puppet whom he constantly talked to (it was chosen for me by the GM), although I have heard better since. Split personalities are easy to come up with and roleplay, and they can be very entertaining too. I once met a son of Malkav with a second personality that was a Vampire Hunter. It really upset the rest of his party when someone in the background whistled for a taxi and he proptly began trying to kill them all!
If you want a place to set up home, think of your characters background and dementia. A security guard may have a thing for abandoned warehouses, while an ex-teacher (an excellent possibility for an insane character) would prefer to live in a school. Think about how Malkav's generally hark back to their mortality in a lot of cases.

Hope that helped.