Being a homeless vampire definitely presents its own true challenge, considering the risk of dying to sunlight alone.
To give something to do, then you need to give your vampire a goal. Instead of just homeless, go rags-to-riches.
Basic:
- Have the klepto trait, and one of the first powers to take would be Vampiric Entrance. Raid houses during the day, putting residents into hallucinations or mesmerize them, and take an item. Rinse and repeat, and then sell the items at the flea market to pay for necessities. Instead of building on the empty lot you need as a "residence," save up to buy another lot that you can build beforehand with all the things you'd want for your vampire.
- Doing all of this while avoiding becoming a vampire-kabob will be just about enough, but there are things you can add to jack up the difficulty. For one, have your vampire have the Good Vampire aspiration, so they would have to get plasma packs and harvest plasma fruit to get by. Trying to be good would mean avoiding stealing, as well, so finding another source of income would be necessary. One common rags-to-riches rule is never just selling items for money, but instead selling directly to sims through a store or flea market. As an easier way of doing that, I modified one of the shops in Magnolia Promenade to be a Pawn Shop and then pretended the items I was selling directly for money was instead being sold to the pawn shop. But the sim has to be physically there and at the counter.
- For more challenge, go for the worst downsides as you level up. Uncontrollable Hissing does a great job at killing social relationships, and might just make it harder to sell at the flea market.
- If selling items that way does start feeling tedious, then I would say taking on a part time job or odd job would be allowed. For one thing, imagining a vampire flipping burgers is definitely amusing. But no full time jobs. There is no business that wants a vampire around full time, short of one they have started their self.
This should give you a good base to start from. As I said, give yourself a goal when doing a homeless/rags-to-riches challenge. Either building a house on their own empty lot, saving up to buy a pre-built home, or even marrying into money(such as marrying Judith Ward for the highest challenge) are all options. But once you pick a goal, stick to it. It will mean more to you having achieved that as opposed to flip-flopping.