Start off with a week or two. A month is generally a safe maximum. Usually, your boss at your day job may be bending over backwards letting you off for an entire month. Anything more is probably pushing it. Also, consider the fact that you might get homesick.
Cheap motels are the best.
If you have relatives who live near the city you plan to play in, call them up and ask if your band can have the floor of the living room or garage for the night. The last resort is sleeping in the van, but it's been done plenty of times.