If noise is a concern, look for a small complex with all or a majority of one bedroom units (and no three bedroom units) without a pool. This tends to weed out most folks with kids.
I bring something to check whether the outlets work (hi, cellphone!)
Check the state of the appliances; if there are any plugged-in items, check the cables. Seen peeled or burned cables way too many times.
How well-maintained are the common areas?
Something which got me burned once: I’d seen an empty apartment with huge windows and blinds. Then when I moved in, the blinds had been taken off 
Turns out they weren’t part of the lease, which was completely stupid since they had to be custom-made… well, stupid on paper, I’m sure the guys who made them were related to somebody in the management agency 
One thing I never considered when I found my apartment was which side faces hot afternoon sun. I’m thankful that my bedroom is on the cooler east side but I’d love to be able to sit or grill out on a shaded east-facing patio with a beer after work and I don’t get to do that- it’s a bummer. If it was a bigger patio I might be able to fit a table/umbrella or something, but it’s really small.
Street and traffic noises, some thoughts:
If your unit faces the street you may experience a lot of this, but you typically get a greater feeling of privacy than if your windows face the building next door.
Being near schools means an extra load of traffic when they begin and end their day, but it can be tough to find a place not near a school, given the typical population density of areas where you find apartments.
Don’t rent a unit that overlooks a drainage ditch in the road, vehicles driving by will either zoom right over with a loud kuh-THUNK, or else drivers will slow down for the ditch, then downshift and accelerate once they pass. Both are noisy. We had this in front of our old place; apparently it’s a natural rivulet or watercourse of some kind and the city can’t seem to fix it.
You also don’t want to be on or near “the shortcut to the freeway”, or the alternate surface route, or the handy left-turn-arrow signal that everyone uses to get to the freeway.
My most difficult apartment hunting was in New York. If you don’t make pretty good money, you’re satisfied with something in a halfway safe neighborhood with less than an hour commute to work and paying less than half your salary in rent. When you’re a couple, the commute part can become more difficult. Otherwise, location has been the big thing for me, along with AC.
That sounds like quite the place. Where do you live?