Hi gpapadop,
No replies to your post yet ..... so here goes!
FWIW, I'm a little suprised to hear such a long trip to Madrid and suggest you reassure yourself that this city is optimum for you and your family for 5 full days. To be completely frank I'm not certain that Madrid is amongst the most popular European capitals for visits .... and you're coming a long way!
So far as where to stay - I see you're a PC member, suggest you consider upgrading yourself to Ambassador and consider booking a club room at the IC. This will give you and your family breakfasts and refreshments all day and a nice bolt hole for your trips back to base as unless you're buying a suite your going to find any room a touch cramped. I think the IC lounge could make a real difference to your trip and as you're extra room rate is covering 4 people to use the lounge I think it's good value. There's also a afternoon tea and soft drinks all day happy hour each evening, snack for much of the day ie normally lunch and evening ..... and your membership pack will give you a voucher for a free weekend night and a potential upgrade to your MAD booking. I wouldn't say that Madrid is a gourmet destination and you may find the lounge will be more useful to you than you might think now whilst you're planning. (Not suggesting you won't find good places to eat .....!)
You can also hunt out Friends and Family rate - though make sure you use the weekend rate if using the bogoff cert. The hotel is close to a metro station although it isn't located right bang in the center - it's close enough.
Personally I'm not fond of Madrid and have no plans to return so I'm not placed to recommend things to do with any sincerity other than to do the tapas bars (might be tough with the kids) and try a calamari sandwich which seems to be popular after church on Sunday ......
Enjoy your stay and by all means ask any more questions you may have.