In college I lived in University Heights (Park at Madison), then Normal Heights (first Felton just south of Adams, then 36th, just north of Adams.) Then I moved downtown near the El Cortez.
All of the neighborhoods had an edginess – especially downtown. But this was 20 years ago, LOL. (Horton Plaza came online while I was living down there… it was before the convention center, etc.)
I think in Normal Heights the key is whether you are north of Adams or not. It gets pretty nice north of Adams… It gets sketchier the further south of Adams. University Heights, west of Park, has very nice pockets… I have several friends who live there.
I like Hillcrest a lot. Again, location is everything… Lots of nice little pockets. Lots of restaurants and shops.
All three neighborhoods are urban – which is not a bad thing… it makes for walkable neighborhoods. But it also means more people, more challenging parking, more noise.