I've put the following together over the past 3-4 years. So much of what's out there on emergency preparedness takes for granted that you have an outdoor space of some sort to use a grill or camping stove safely, space to run a generator, a garage/shed to store propane or kerosene for a space heater. Many urban/suburban apartment/condo dwellers have none of these things. This is exactly my situation.
I rent a small 1-bedroom condo, first floor, in an apartment-style building (unit entrances off a common hallway), with no balcony or patio.
Cooking in an emergency was really my most vexing issue, since the usual camping stoves cannot be used safely indoors. I have an electric stove. If I had a gas stove, I would just light the burners with a match. After some research, I hit upon Sterno. Yep, the same stuff you see keeping food hot at banquets and parties. It's a gelled alcohol product. Safe for use inside, safe to store. There's a little folding metal stove to get to use with the Sterno. I can fit a 2qt stainless steel saucepan (from my usual pots, not a thin camping one) on it easily. I can boil two cups (16 oz) of water in about 9 minutes. It will heat up a can of soup, ravioli, or stew in about the same time. I put it on top of one of the burners on my glass-topped electric range, so I don't have to worry about melting the countertop.
Sterno isn't for actual cooking, it's for heating things up. So, water and canned goods. Get some sort of thermal carafe to keep water hot for future use after boiling. A good thermal mug for keeping your hot beverage hot for a long time is good. I got this one at Target. At $20 it's not cheap, but it keeps my tea hot for at least 8 hours, plus it can go in the dishwasher (lots of thermal mugs can't).
http://www.amazon.com/Thermos-Stainl...nd+thermal+mug
Sterno stove (you can get it cheaper locally at Walmart, about $7):
http://www.amazon.com/Sterno-Single-...s=sterno+stove
Sterno fuel 2 pk (cheaper at Walmart or other stores locally, $5):
http://www.amazon.com/Sterno-7-Ounce...W6XTF0NNR64PZR
Since you don't need to light a huge space, this Coleman Micropacker LED mini lantern is great. It's enough light to read or write by. It takes 3 AA batteries. I have one, want to have a spare. $10
http://www.amazon.com/Coleman-MicroP...attery+lantern
If you have older battery lanterns, you might want to consider getting an LED one. They are much more power efficient.
I've found that the flameless LED tea lights available everywhere are great for leaving in the bathroom if you want to have some sort of light overnight.
Headlamps are great for doing things hands-free or even for reading. Check out your local Target/Walmart in the flashlight section. The Energizer brand ones that take 3 AAA batteries are good enough for this use, about $12.
I like having a hand crank flashlight, too. This one is excellent. I got mine at Target - $10.
http://www.amazon.com/Energizer-Weat...ank+flashlight
I have both a battery-operated radio (2 AA) that's about 9 years old from LL Bean that's my everyday radio. You can get a small radio like this for about $10 at Walmart.
http://www.amazon.com/Sony-ICF-S10MK...words=am+radio
I like having a hand crank radio, as well (I like listening to the AM all news station). You can go to Walmart or Target and there are a number to choose from, or check out Amazon.
For summer, there are a number of battery-operated fans.
Unfortunately, there are no non-fuel heater options in the winter. The best idea I've heard is: under a heavy comforter or in a sleeping bag, use a Nagalene bottle filled with very hot water and closed tightly. Use as a hot water bottle.
Something else to think about is how to charge your phone, especially if it's a smartphone (news via the web). This was a major issue for people when Hurricane Sandy hit. There are any number of small battery backups you can get, which can charge your device up to 4-5 times. I just ordered this one:
http://www.amazon.com/gp/product/B00...?ie=UTF8&psc=1
One important bit I took away from reading about the experiences of people during Sandy: one blogger commented that most people she knew used their laptops to watch movies until the battery went dead. She figured out the laptop was more valuable as a way to charge her laptop. You might want to fully charge laptop, and with a phone charge down around perhaps 30%, see how long it takes to charge your phone, and if you can get a full charge off laptop.
For longer term use, you might consider this:
http://www.amazon.com/dp/B00KIXSXWQ?psc=1
There are other battery-powered car jump starts that even have 110V electrical outlets, as well as a USB port or two, on them. You can get those at the big box home improvement stores. Prices seem to be around $75-$150, depending on how much capacity you want.
And of course, you want not electrical entertainment - books, games, etc. I do keep a fully charged Kindle Paperwhite, but I also have a number of paper books. I loved Solitaire as a kid, but I've played it for so long as a computer game, I'd forgotten how to play it using actual cards. I got a pack of cards and relearned how to play it "manually." ;)
I also stocked up on toilet paper, paper towels, toiletries, OTC meds (preferred pain medicine, Immodium, allergy meds), in addition to canned goods and water. I've got the toiletries and paper products stored under my bed. Other items are in a plastic tub in the closet.
As I've learned, don't advertise what you have in the way of "preps." Depending on your neighborhood (especially if you're urban), if the power outage was long enough, folks might decide to help themselves to what you've got, hurting you in the process. I'm prepared to defend myself (two 9mm pistols, concealed carry permit, and a good amount of training including the legalities of self-defense), but many people are uncomfortable with that.
Just thought I'd share what I've learned over the past few years, as I know other apartment dwellers who think they can't do anything since they're apartment dwellers. There's much more you can do than you think. Storage space might get to be an issue, but you can get creative (hence, the under bed storage).
