1. Get me Home/Get Me To Work quick links. It takes your current location as starting point and tells you your options for going home/work.
2. You can configure it to monitor your subway line during commute time (7AM to 10AM and 4pm to 6pm) and it will notify you if the subway is delayed for any reason. I use line 6 which breaks down more often than I want and thanks to the App, I can take N/Q/R if Line 6 is down.
3. The way 'Get Me Somewhere' works. In addition to being able to type an address, you can move the map around to point the destination pin to a particular point in map. It's hard for me to explain but it works amazingly well especially in NYC where people often go by cross streets and don't have the actual street address.
I completely agree with author that Citiymapper has an exceptional UI/UX.