Leave a general list of expected stops, or at least the expected arrival time at a final destination, with someone trustworthy at home. Admittedly, you may not make those stops at exactly those times, but it's a good idea to make sure someone knows where you're supposed to be at least part of the time. Make sure that person has the names and phone numbers of everyone in the party. Call them if there are any major changes in your trip.
When you arrive, you might want to call home and leave the number of the hotel where you're staying, in case there's a problem with cell phones.
Take an ATM card with you so you can get cash if you need it. A number of institutions have connections with banks all over the US. Many of them charge fees for withdrawals, but it's one way to have access to cash most of the time.
Take road maps of the areas you expect to visit. You can often find your way by consulting a map if you can't find anyone to ask for directions.
Carry ID with you at all times. During my last trip, my parents and I were asked for drivers' licenses or other ID whenever we wanted to charge anything on a credit card. This is especially important if you're leaving the country for any length of time. If you know you're traveling to a foreign country, file the paperwork for a passport now.
Label your luggage. Labels can be purchased in various places (often where you would buy luggage -- convenient, no? :wink: ) The tags should list your name, address, and a contact phone number in case the bag is misplaced or you turn up missing. At the very least, write the information on a slip of paper and stick it in the bag somewhere where it won't get lost.
Travel-sized items such as toothpaste and aspirin are available in many stories, including Wal-Mart. It's easier than hauling the full-sized stuff around.
If you want good places to eat, ask the hotel clerk or a store clerk where s/he would take his/her family to eat for a reasonable price. You'll often find really good local restaurants you wouldn't otherwise try.
Look for hotels that offer breakfast included in your room rate. You can save some money that way, and the food is fresh each morning. Most hotels that do that will offer an array of foods, so finding something you like for breakfast isn't difficult.