The most useful, and predominant item you will need. You need it to shower, to wash your clothes, your dishes, and filter your body. Where can you find it? Just about everywhere. When you cant find it, you will be in trouble. Therefore everytime you are near some, take some. Always have as much water on you as you can carry. There is never too much water you should have on your body. Fill several nalgines, (classy water bottles) or any bottle you can find with it. You never know when you might not have any access to fresh water.
Drinking water can be found in libraries, schools, resteraunts, grocery stores, parks, laundrymats shopping malls, and some fresh water streams (if need be iodine or chlorine tablets can be used to purify water you feel might be contaminated which you can pick up at any army navy store ((army navy stores are a homeless persons dream shop, scour them with great pride.)))
Water to wash up in can be found in any public place. I prefer handicaped restrooms to be used as bird baths (sponge baths) as the privacy and space can be idealy used. But you can wash up just about any place you have access to some water. make sure to hit the private parts when possible, these places (under arms, groin, buttocks, feet, and face) get the most dirty, and you always want to have a clean appearance. Clean bums get more privlidges than dirty ones. Nobody likes oder.
Showers can be found for a few bucks at YMCA’s, colleges (sometimes) parks, truck stops, and public pools. You can also find a friend rather easily who might be willing to let you shower. Couchsurfing.com is a great place to start.
Washing your clothes can be done in a clean river, a laundrymat, a pool at night, a bucket of water, etc.