Yes, I'm in Bangkok now Kitty. We arrived here Wednesday evening after a leisurely drive back from Hua Hin where we'd spent 5 days.
After unpacking we got a taxi down to Silom and went to the supermarkets - boring I know but we fancied some vegemite.
We had a bite to eat at a little place on Silom Rd. - Bug and Bee (!) just near steps to Saladaeng BTS station on Patpong side.....they serve all sorts of things in crepes... curries, stir fries, spinach and bacon etc. - would appeal to kids too. You can sit downstairs in the shop or in the nicer part upstairs.
Today I'll get a haircut and do some shopping at Central Department store in Silom Complex - often a lot quieter than other malls.

I think shane has given you some good ideas - maybe a bit busy with kids in tow but you have plenty of choices anyway.
Because you only have a short time and want to fit a lot of things in, I think the trick is to combine things that are in the same area + do a bit of 'busy' stuff and a bit of 'quieter' stuff such as a boat trip along the river followed by a bit of shopping, then dinner and then back to the hotel.
Going by boat along the river is a nicer way to get to the palace area than going by taxi. You can see boats and barges along the river + have views of riverside hotels and temples. It's a nice relaxing thing to do.
Get the BTS from Siam and go all the way to Saphan Taksin station at the end of the line. The public boats are the ones you want and you buy the tickets just downstairs from the station -120 baht for a day pass I think - you can get off at any stop and get on a later boat and get off somewhere else.
When you arrive back at Saphan Taksin, you can get off BTS at Saladaeng which is right near Patpong - you can shop at Silom Complex and/or go to the night market. By doing this, you've combined the palace + temples with perhaps lunch at one of the riverside restaurants, a river cruise and shopping all in one convenient circle trip.

Re money....When we came to Bangkok, I changed some money at the airport - yes, the booth was open at midnight - and next day we went to the ATM while out shopping.
All accomm has already been paid for so the cash has been used for everything else (lunches and dinners, bars, taxis, limo to and from Hua Hin, small purchases and top up for mobile phone sim card).

One word of advice for the adults ....... bring minimal toiletries... they weigh a lot and will use a lot of your baggage allowance. Instead just bring whatever is 'must have' for first night. On your first shopping trip call in to Watsons (chemist) or 7-11 (they're everywhere on the street and also Watsons in MBK) and buy whatever you need - shower gel, toothpaste, shampoo and conditioner, hair products are all available at these places.
You can get everyday brands like Dove, Pantene, Sunsilk, Nivea, Ponds etc - all much cheaper than back home and when you leave, you can leave them for the hotel maids (more room in your case for important stuff!) High end toiletries and skin care (Shisheido, Lancome etc. can be found at cosmetic counters and stalls in MBK (2nd or 3rd floor).