Buy a tiny plot of land in the woods and build a cool little cabin by hand.

If history is a guide, the nicer, established locations close to city center will command a rent premium.

There is nothing to say that you wont strike gold and find the perfect tenant who pays enough to cover the mortgage, but it is much easier (especially if you don't mind college students) to charge a premium rent that cash flows hundreds of dollars into your pocket every month if you find a property within the city limits.

But if the urine is soaked into the wood it will always smell - and it is a health hazard.  

I mean for CA, my insurance premiums alone ran 15k before I even landed on my first project, another 5k to acquire the license and entity.

When my friends and I graduated college many of them got 1BR/1BA units right downtown, but they paid a huge premium.

If you are worried about the liabilities surrounded with purchasing the property under your own name, you can increase the limits on your insurance policy similar to what @Brian Ellis said for a relatively low cost - especially for general liability.As per @Benjamin Haberman's approach, purchasing an umbrella policy will offer you much more protection than merely increasing the limits on your primary policy, however this will come at a premium price.Both solutions are viable; it just depends on your risk appetite and annual insurance cost your comfortable paying.

@Kevin Wood Thank you, I will keep that in mind!

Needs some work, dated bathroom, very plain)   I am hoping my new LVP wood flooring, high definition laminate counter tops, new vanities, fresh paint, and more attractive exterior bring me higher rent.We are currently rehabbing with the help of a skilled worker from a big contracting company taking us on as a side job.  

Option 2 is cheaper (one premium instead of two).