There are so many variables. New or used and how much did it cost to purchase a TT? What are you going to tow with? Our Avalanche only gets about 15 mpg normally, and that is reduced to 10 mpg while towing. Remember if you drive toll roads your cost will increase due to the extra 2 axles.
How much you save depends on how much you camp. I know a lot of people that have TTs but only use them 1-2 times per year. It also depends (sans TT) on whether you would be staying at a Motel 6 or a Radisson Inn.
I like to be outdoors and camp, not stuck in a motel room. So I don't really focus on any cost savings. When we stay at hotels, it is probably an average of $100/night, while CGs can be $40-$60/night. If I camp 20 nights a year, then that is a savings of: 20 nights x $50 = $1000/year.
Depending on how/where you eat, you can also save on food if you cook at the site, which is usually not an option in a hotel. This could be a substantial cost savings.