As you can see from the lengthy discussion [that is, if you are still reading here
], fulltimers hold their overall costs down by using a lot of free or very low cost campsites. If you look for them, there are quite a lot of low cost or even free campsites available in town and county parks, federal lands, and businesses that are seeking to attract you for other purposes (e.g.casinos). You can also reduce costs with long term stays, which are typically steeply discounted. Even a week long stay usually garners one "free" night, i.e. you pay for six and stay seven. Another thing that helps is senior citizen discounts at state and federal parks, sometimes as much as 50% off. When comparing to your current home expenses, remember that this cost include utilities and there are no property taxes to pay. The extent to which you use the low-cost options will dictate whether your average daily campsite expense is around $13 or more like $20-24.
As Don says, your costs for fuel, restaurants, sight-seeing, etc. will depend very much on your personal wants and needs. You will likely travel at least 6000 miles/year and 10-12,000 is probably more likely. In the first years when you are avidly traveling around to see this great country, 16-20,000 miles/year is not uncommon. Fuel and vehicle maintenance costs obviouslt depend on mileage. Fuel economy will range from 7 to about 13, depending on type and size of vehicle and how heavy your foot is. 7-10 is probably typical for a motorhome and trailers usually average a bit higher, perhaps 10-13 mpg. RV fuel economy is generally quite sensitive to speed becasue of the wind resistence of large vehicles.
You need insurance on your self and on your RV. If you currently have two vehicles at home, the insurance costs for a motorhome + a towed car or a truck + trailer will not be much different than what you already pay. May even be less if you are currently in a high insurance cost region. You will also need to maintain separate personal liability coverage which is currently included in your home owners or renters insurance. This is usually included in "fulltimers" RV insurance packages and adds around $150-200 per year.
Health insurance can be more expensive, especially if you now enjoy a low-cost HMO in your home town. Most fulltimers try to maintain doctor and dentist relationships in some area (not necessarily their old home town) and visit there 1-2 a year to handle all routine medical & dental needs. Costs are about the same as you would have if you were not full-timing. However, if you need continual routine access to treatments as you travel, chances are that both insurance and out-of-pocket costs will be higher than you now pay because health plans that provide coverage across the country generally cost more than more restirctive plans.
Some fulltimers choose to maintain property somewhere, a "Home base". If you do that, the cost of maintaining it is part of your annual budget and makes some of the RVing costs add-ons instead of ini-lieu-of home expenses. Fulltimers with home bases usually buy something modest in an inexpensive area (there are still lots of them around) rather than attempting to maintain a large "city home". Your choice in this matter is a major factor in both costs and lifestyle and is something you need to think about. Options range from a lot where you can park your Rv and live in it to a cottage or a town house somewhere and maintenance costs (including taxes and insurance) can be anywhere from a few hundred dollars per year to many thousands.
Hope this gives you some idea or at least the basis for further thought and questions.