Firstly the generator, even the small one like a 1 or 2KA suitcase generator, is most likely going to run on liquid petroleum. It is very dangerous to store this fuel inside any property or on a balcony apartment.

I would go for bottled LPG or even industrial Propane bottles. These are reasonably safe if you follow the safety guidelines You can purchase lanterns which can be powered from butane or propane. You can purchase gas stoves, which will work indoors, but once again they will need Flame Failure Devices (FFDs) fitted for the safety aspect. Get a CO detector/alarm, they are cheap to purchase as well.

To improve cooking efficiency get some of the cooking pots/kettles etc with heat exchanger bases.

Your small electronics powering requirements could be resolved using a small Solar PV Panel i.e. 60W, a charge regulator and a battery. i.e. preferably a non spillable type such as sealed AGM SLA type.

If you desktop computer draws 200-300W then get a notebook that draws 12W. Reducing the load on lighting is now easy to do. i.e. a 100W incandescent light bulb can be replaced with an emergency 3-7W LED type. i.e. you would go from 1500 lumen to 250 for the 3W or 450 lumen for the 7W.

You could even get a biolite Stove for the balcony if folks really can't stand being withdrawn from the 'Matrix'. You will need a good quality survival knife to chop up the apartment furniture to fuel to the biolite stove to keep the iPhone charged, whilst you make a nice cup of tea to sooth the panic of not being able to keep up with the latest twitter or facebook feed.