@Nick S. The area immediately around Crown Hill cemetery is rough, as evidenced by all of the houses under $50k currently listed for sale. I think most of these are SFH with some duplexes mixed in. This is generally the case from 30th to 42nd between MLK and Meridian.
Meridian serves as a bit of an East / West barrier. When you get east of Meridian, the neighborhood changes. You will see large, historic homes. There is some revitalization happening there but it still has some rough patches. See: post from @Chris Davis and Mapleton Fall Creek. Also some more duplexes mixed in here.
38th Street serves as a North / South barrier. Generally speaking, nicer homes N and rougher S. Evidenced by $800k listing at 40th & Penn and $320k listing at 39th & Central. This is Oliver Johnson Woods area. Move slightly North into Meridian Kessler - prestige, mansions, historic homes, high prices, beautiful neighborhood.
Jump back over to Crown Hill, go north of 42nd, and you will be in Butler Tarkington. College campus nearby. Some similarities to Meridian Kessler but at a lower price point.
South of 38th, it gets rough again when you cross E of Fall Creek Parkway.
Warren Park - between 10th - 16th & Arlington - Shadeland ... I think the bullet holes in your property comment might be over dramatizing it. Might be an OK area depending on what you are looking for. SFHs. Small ranch homes. More of a rental area. Some apartment complexes in this pocket have some crime issues. Pleasant Run Parkway runs along the creek and is scenic with nicer homes.