I know that Pilsen is a popular neighborhood for UIC residents and med students due to the Pink line and you'd be more likely to find a 2-unit under 500K there.

These are speculative, but here is somethings to search for: 1) A new national park/monument that takes most of a day to experience (something like smokey mountains, Yellowstone, yosemite, Joshua Tree, Bryce, Zion, grand canyon, etc, but new) 2) a newer university in the area that has large funding allocation (UC Merced: By far cheapest area with a UC university) 3) new tourist attraction such as presidential library, amusement park, etc. 4) a tourist attraction that may not have hit its peak (Havasupai popularity has grown at stupid pace, Antelope canyon is crazy popular but Buckskin is not and is in many ways superior, etc.).  5) A city that for some reason has depressed values. 

Correct me if I'm wrong, but from what I read in the fine print of my homeowners insurance policy, if anyone is injured on my physical property...even outside of my actual house...the liability portion of my homeowners insurance covers that.

Plenty of other similar providers like this I am sure, but they are a couple of the most popular ones.   

Vacation/2nd Home Loan: This product has been increasing in popularity due to investors only having to put down 10% deposit on the next property.

Seller financing, private money investors, and popular location, along with some good options to analyze - especially with the two city lots/parcels.

Cozi is popular.

Her mother wacked herself in the head on a open window on the exterior of my home and injured herself and was interacting with me and several times told her daughter what to do next etc..

Not sure where you are investing but below are some of these guides for individual markets that are popular with investors.The Ultimate Guide to Grading Cleveland Neighborhoods_The Ultimate Guide to Grading Kansas City Missouri Neighborhoods_The Ultimate Guide to Grading Birmingham Alabama Neighborhoods

I say the same company because, if it is one property and someone gets injured outside between the buildings, there will be a question of which policy responds.