affordable Amsterdam

You might look into some travel guides for recommended accommodations in Amsterdam. Also see if any Amsterdam B&B's are listed on Rick's Graffiti Wall for Heroic B&B Experiences. I usually stay in a B&B out by the soccer stadium in Amsterdam North and take a tram into the city--15 minutes. The city is so large that it has virtually any accommodations you require. You can always find rooms in Hotels.com, Venere.com and AirBnB.com. Also Expedia and Orbitz.

Agree Amsterdam is tough, and your budget for four people is not great either, but i would try Venere.com , Priceline or Hotwire, and most importantly , double check for reviews. I always check on tripadvisor.com, just google hotel name and "reviews" .
Amsterdams cheap places can be rather, , er, shocking to North American standards, rooms WILL be tiny, and many have no elevators, and soundproofing, ha, bring earplugs. There are big nice hotel rooms with modern everything, you will not find one in your budget range though, so consider it an experience in Europeon hotels,, and just settle for clean and decent area. Rooms for 4 are hardest of all, so many places will only have one or two such rooms if at all, so they fill fast and they are harder to find. Also suggest you go on various forums and ask for suggestions. The hotel we stayed it cost more, ( not a lot more, but it was a double not a quad , so no going to be helpful) . I think you may have to try and budge up the budget a wee bit, once you convert that to Euros its not very much for a room for four people, not even in the city I live in! Save on other places you are staying in ( like Rome, and Paris I hope!) Good luck, and do lots of research, you will likely find something in your range give or take a bit, but its just not as easy . Good luck.

I'm confused - you ask for under €100 a night for a family of 4 but you say you are 10 of you... Have you considered apartments in each of your bases?

Hotels in Amsterdam are expensive, especially on the weekends. Mid-week is actually cheaper. If you don't mind staying in the outskirts, hotels near the RAI convention center are heavily discounted between events. For something in the city center check out the RHO Hotel. I believe they have large family rooms and it should be within your budget: http://www.rhohotel.com/

We stayed at Vondelpark Hostel. It should be about your budget. We stayed in a room with six beds at a normal hostel price per bed. We were a family of five. They said they would try to keep the room just for us but no guarantees - the sixth bed was occupied when we got to the room. It wasn't bad, close to the museums and easy tram to downtown, the place was clean enough and not too loud. They don't allow pot in the building - which means you walk through a cloud out front to get inside. Vondelpark is across the street. It's a decent park but, again, too many discarded drug items strewn around and small groups of people smoking pot everywhere - welcome to Amsterdam.

Try hotels in the Zuidas area. It is a business district full of modern (post-2000) buildings and some cheaper hotels. You will need to use public transportation to get to/from central areas where 90% of tourist attractions are (15 min average). You could also try renting an apartment, especially if you are willing to compromise a bit on location and use public transportation.

I don't have specific suggestions, but I can confirm that you're not "missing something." I found that Amsterdam lodgings were not only pricey, but also not good value for money. The city is popular year round (especially on weekends), many of the places have a relatively small number of rooms, and many places are listed in multiple guidebooks. So, following the principles of supply (limited) and demand (high), rooms are expensive and hard to get. Your stated budget is about €115 euros a night for a room that sleeps 4; I paid that much for a room that slept 2 (and it wasn't luxurious either). I agree your best bet is looking outside the center, just making sure it's on a convenient tram line to more central attractions. I'm also confused by your statement that you have 6 adults and 4 kids, but want a room for a family of 4. I hope you were planning on getting rooms with sleeping space for 10 people (this will require 3-4 rooms). Rooms in Europe do not sleep any more than their advertised number; you don't get two king beds where you can put extra people. The rooms and the beds are small (particularly in crowded cities like Amsterdam or Paris), and the fire laws mean that the owners really do care about extra guests, and won't go over the legal per-room occupancy limit. So, you will need several triples or quads, and these can sometimes be hard to find on hotel booking sites; you may need to e-mail the hotels directly to check availability.

I scanned the other replies quickly, but I saw no one mention booking.com. When I was recently looking for hotels in Amsterdam, I noticed some listed rooms that accomodated 4 people or more. I just checked and discovered that you can click on "more options" in the "guests" search box and list exactly how many adults and children you want in the room. You can choose other filters as well after you get the list. To see prices you will have to put in real dates. You can sort the list by "review score" and even choose the scores to be from families with older or younger kids. The more specific you get, the more that initial list of more than 600 hotels will be cut down. If you haven't already tried booking.com, it might be a help. I'm not sure about Amsterdam, but apartments and B&Bs also showed up on the booking.com list for me in other parts of the Netherlands, even though the main title is "hotels". Like others have said, depending on how long you will be there, an apartment might be a good option. But, they have the same limits on numbers of people that the hotels do. Today, $150 is only about Euro 113, so good luck with your search. That is very cheap in many parts of Europe -- especially for 4 people.

@Lo: many hotels can "join" 2 adjacent rooms by opening a door between them. So they can advertise what are in fact 2 rooms for less than the price of 2 double rooms and get some extra business catering for the family crowd.