Upvote:2
Funnily, when backpacking in South America we regularly ran into hostels that had families staying there - like the one (Che Legarto?) in Iguazu - the kids kept hogging the pool table ;)
However, another option for you could be AirBnb - I was skeptical at first but it's now got a huge selection in most places, and includes rooms and entire houses for rent.
Another option is booking.com - great for searching by person/room size - you can say, sort all the results by price for those with 4-bed rooms. And it regularly seems to have some quite useful sales.