With multi-story and possibly apartment buildings; you can attempt window-drop kills, landing in dumpsters, filled or not (as previously suggested (depending on what's in the dumpster can improve odds of survival; like a dumpster full of soft garbage or mattresses could give you +50% to survival, whereas hard garbage, glass, or scrap metals (like fencing or furniture) is -75% to survival, added on top of damage done by a fall of whatever height; intelligence affects fall accuracy)), or fence kills (nothing like skewering your target with a wrought-iron fence; stair-dropping, or even restraining your target onto a lightning rod and waiting for a storm to fry him.
If allergies are an eventual feature; we can get a beehive, toss it into a victim's house whose allergic to bees, and watch as they get stung apart. You can also try to unleash some black mold or asbestos if you can get a hold of them onto your sleeping target. Heck, got a pet tarantula or scorpion or snake, let those loose and poison your target with venom as well. If you also have pet doberman or rottweiler (police can also sic these guys on you as well), send them to chase or ambush your victim and bite off limbs.
EDIT:
Also with apartment buildings or multi-story buildings, we need fire escapes as a method of entry/exit, as well as a jump system to hop from balcony to balcony (or building to building if they are close enough to each other) at least jumping 1-2 tiles, up to 3-4 if particularly strong or nimble, with maybe a running start. Also inherent with being smart enough, your character can automatically tuck and roll upon landing, especially if the jump is from 2 different heights (particularly -1z) to minimize damage upon landing. It would also help in evading police. Heck, it could double as a parkour challenge.
EDIT EDIT:
I guess if you also want silly ways of offing someone, have the ability to drop stuff on people from 1 to many stories above them. Even go as silly as throwing water (or blood) balloons at your targets; then when they least expect it, a rock.
For additional fun, act suspicious enough for your neighbor to snoop around your house, and go morbid Home Alone on them, dropping limbs from above, and having the victim slip and fall on their back because the floor is riddled with eyeballs and other random stuff; place random flamethrowers and heated doorknobs, tar and feather them, and drop a tarantula on them. Oh, and don't forget broken glass next to the windows, and slippery ice next to the doorways. When the police start chasing you down, continue the assault and use the zipline from the top of your home to a nearby treehouse.