It depends on where you want to live. West Los Angeles is hugely expensive; Hollywood or the Mid-City has more variety in terms of prices. You mentioned North Hollywood, which is in the San Fernando Valley. In general, rents in the Valley are cheaper across the board than in the rest of the city (in the sense that, say, a two bedroom apartment there will probably be cheaper than a two bedroom apartment of comparable quality in the rest of the city).
North Hollywood specifically has a pretty wide range. Their are older buildings that date back to the 1950s and 60s where you could probably get a 1 bedroom in the $1,000-$1,200 per month range. The neighborhood has also been gentrifying for the past decade or so, and there are plenty of renovated lofts and industrial spaces that could easily go for two to three times that. It's also a bit of an uneven area in terms of crime and overall quality of the area. Like I said, it's gentrifying and has the typical symptoms that come with that.
Anyway, I'm actually a native of the Valley and lived there for about 99% of my life so far before moving a year ago; so I know it pretty well. Feel free to ask any other questions you may have about the area.