The Jordaan is nice, as is the area around The Nine Streets, but The Jordaan is not the only decent area to stay in the city. Helmersbuurt and De Pijp are both good neighborhood areas full of locals, decent selection of shops (including several grocery stores and also outdoor food markets like Albert Cuyp), restaurants and easy access to transit, yet still a quick walk to many major sightseeing venues. You may actually score a larger apartment rental in these neighborhoods than you would in the Jordaan which is extremely popular with tourists - something to consider as you are traveling with older teens and not small children - so 4 people in a small studio can feel a bit tight.
If you have a healthy budget and don't mind being in small spaces, another option might be to look into houseboat rentals - some of them are amazing and have fantastic outdoor space on the deck of the boats which is great if you score decent weather during your visit.
Google Street View can give you an idea of your surroundings - you should check it before you book a place just to see what's nearby. And pack light if the apartment building has no elevator. Staircases in Amsterdam can often be very steep and if a rental says it's on the 1st Floor, that's really the 2nd Floor in U.S. terms.
If you decide that you do want the amenities of a hotel stay, The Times Hotel has one canal view suite that encompasses two levels and accommodates a family of 4. Fantastic neighborhood - right in between The Nine Streets and the Jordaan and within walking distance to Centraal and multiple tram line stops within a block or two of the hotel.
