My own experience
Priceline - Great for hotels, not so great for flights (I've had friends tell me of really crazy bookings they've gotten through PL). As long as you're comfortable staying anywhere within the listed neighborhood (always look at the maps) and using a site like betterbidding.com, you'll be fine.
Flight - Agree with other posters that's it's probably better to try to get award travel using a credit card or frequent flyer program, rather than using priceline. Depending on destination your choices may be limited, but Paris & London should have plenty of availability. And also agree about BA 'taxes, fuel & fees' ripoff...might as well just pay coach and get the miles on a partner airline.
Lodging - Although I've never stayed at the Sanctuary in London, I've heard many good reports. Paris has a number of good, small, affordable 1 & 2-star hotels and with the Metro, you can pretty much stay anywhere in the city proper and easily get around. I can also vouch for renting an apartment...we rented apartments on a recent trip to Italy and off-season, it's an affordable alternative...don't know about Paris & London however.
Passes - In Paris, we've used the Paris Visite and Paris Museum pass. Depends on how much museum time you want to expose your kids to, but the Paris Museum Pass provides access to 60 museums (including all the biggies...definitely worth it if you're planning on doing more than one a day). Plus there's stuff besides museums included.
Meals - Agree with another poster about prix fixe meals in Paris. If you're not renting an apartment, it's pretty affordable to have fresh baked goods for breakfast, buy sandwich makings and fruit for lunch and then have a prix fixe for dinner. I've been lucky and never had a bad meal in Paris (I've had some OK, not great, meals, but never anything bad. I think it's harder to eat affordably in London, but between fish and chip shops and a nice pasty shop in Covent Garden, we managed to do OK.
DLP - And since you're on the DISboards, you have to take the kids to
Disneyland Paris. It's about a 45-minute train ride from Paris....very convenient...the train station is right at the park entrance.
Have fun. Paris is one of my favorite cities and there's so much for kids to do there.
PS. You and your kids should learn a few words of French before you go. Friends have told me stories of rude Parisians, but I've never had any problems. Always enter a shop with a 'bonjour monsieur' or 'bonjour madame' and ask 'parlez-vous anglais?' rather than 'do you speak english?' I was scolded once for bringing my wet umbrella into a shop when there was an umbrella stand by the door...shop owners can be very proprietary but some can take their business very personally.
