If you want to really save some money you might want to consider using one of the following websites.
There are lots of ways to get free accommodation, one of them is couchsurfing where you can stay on usually the couch or lawn of a host for several nights, some people love it others hate it. Couchsurfing is no-longer a non-profit organization so some people prefer to use bewelcome instead, bewelcome is just like couchsurfing, except its strictly non-profit.
Now if you don’t mind watching someones pets or cleaning up the house and doing a bit of general maintenance there’s also
And if you just can’t find a place anywhere else there’s Camp in my Garden, where you can organise to camp out in someones garden, not exactly my pot of tea but I’m sure some people must enjoy it.
If you don’t mind putting in a bit of work you can always get free accommodation via WWOOFing, this is where you work, usually on a farm in exchange for accommodation and or food.
If you have a really long stopover and you can’t/don’t want to pay for accommodation then you should have a look at sleepinginairports, it’s a fantastic guide on how to sleep at airports. It lists bad airports to sleep at and good airports to sleep at and also gives great hints on the locations of free lounges to rest at.