London and Paris (particularly London) are not very budget-friendly places to visit. Eating breakfast in can help some, but transportation, lodging, food, and attractions in both cities are very, very expensive.
Be aware that many buildings in London and Paris are old, and older hotels (which tend to be less expensive) may not have the same amenities you are used to in the United States. Rooms will be smaller and some of the little luxuries you are accustomed to in the US (like air conditioning, a desk and chair in the room, etc.) are not always available unless you're willing to pay.
Paris is 90% atmosphere. Some of my favorite memories of that city are of simple, inexpensive things, like strolling the streets and people watching at a cafe. If you are planning to do the Louvre, really make a day of it - don't just do a drive-by glance at the Mona Lisa and the Venus de Milo! If your kids like history, they would love to take a walk through the underground tour of the original medieval foundation of the Louvre itself. I also recommend the display of Napoleon's apartment.