First, decide what amenities are dealbreakers for you, which amenities would just be nice to have, and which amenities you don’t care squat about. It doesn’t matter if there’s a pool and fitness room if you’re never going to use them. It doesn’t matter whether pets are allowed if you’re never going to get one. But if pets are important to you, then any place that doesn’t allow them is right out (even if they have free utilities and gold-plated microwaves). Amenities I can think of are in-apartment laundry, on-site laundry, balcony, elevator, air conditioning, free heat/gas/other utilities, pool, fitness room, tanning, snack machines, volleyball court, ceiling fans, vaulted ceilings (they look impressive but they’re hard to cool), reserved parking, gated entrance. Decide what dealbreakers you care about and don’t look anywhere that doesn’t provide those options. Treat the stuff you’d like to have as tie-breakers if you can’t decide between two places. All other things being equal, would you rather pay a little extra for in-apartment laundry and free tanning, or go without those amenities? (or whatever) Do you care whether you live on the bottom floor (easier on the knees, but less private, and you can hear people walking above you) or top floor (quieter, more privacy, but the walk can be a bitch with heavy groceries)?
Also keep in mind, a lot of locally-owned properties don’t advertise online at all. By just looking at Craigslist or rent.com, you might be totally missing out on good places to live. Go on a drive and write down the name of every apartment complex you pass, then look them up online and give them a call. Or you could walk in and talk to the person at the front desk. They may still have a website but not advertise online, because it costs too much or they’re uncomfortable with the type of renter it brings (I think a lot of property managers distrust Craigslist, in particular, because of its image).
Ask about the visitors’ policy, and drive by a few times to check out the parking situation at different times of day. My first apartment in college was really hit-or-miss with parking, depending on what side of the complex you lived. I was on an outer corner and never had trouble finding a spot right outside my building. But my friends in a busy inner building had to walk a quarter of a mile if they got home after 8pm. The place wasn’t unsafe, but still… that sucks after a long day at school/work. It was a smart idea for them to buy a reserved parking spot, but it would have been a waste of money for me. Also, make sure to drive by on a Saturday night, to see if there are any loud parties. And beware of renting near a college/university, because students tend to be loud, destructive, and don’t give a shit about noise ordinances. If they have balconies, ask if they restrict what you can do/put on them. They probably won’t allow a grill, but ask if they have any rules about furniture or balcony decorations.
Try to talk to people in your city about places they’ve lived (there are local city forums on Craigslist, if you don’t know anybody). They can tell you whether a place they’ve lived is pretty nice, just okay, or a dump. Going on a tour to the show-unit *won’t *tell you this. I sublet an apartment for about 6 months before finding out there were a shitload of drug dealers in the complex. The place looked alright from the outside, and the show-unit was nice. There was even a private playground. But one side of the complex (not mine) was meth-city. You can also look up reviews online, but take the good ones with a grain of salt (some places pay shills to lie on those). I usually tend to trust a review if it’s fairly well-written, and has a mix of good and bad qualities. No complex is all good or all bad.