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In general, I would expect the cost of building a single ground-launched Orion in the suggested range of 20,000 tons loaded weight to be quite high. First, a substantial amount of R&D would be required to produce an actual design, and confidence that the design would in fact work. Beyond the work done up to the point when the project was historically cancelled, this would take several years and cost hundreds of millions of dollars just for the propulsion technologies and hull design. Then you have to actually build and launch the ship, which would probably take as much as a decade (definitely at least five years even at a very rushed pace). Construction of the ship itself, especially the first ship, would range into the billions of dollars. Plus the fuel, which would easily reach one or two billion. Plus the payload. The payload is the big thing. Orion has a low cost per unit of mass to orbit, but you can only get that low cost by doing a lot of research and construction. Developing and building the first few Orions would easily match the time and cost requirements for the entire Apollo program, and possibly even exceed them. And that's before you've paid for actually doing anything with the ship(s). What if you want to do some interplanetary exploration with them? Well, as mentioned above you are going to be spending many billions of dollars to develop and build additional equipment. You need to navigate the ship, support the crew in space, carry scientific instrumentation, develop and build landers to explore planets with, develop equipment for living on and exploring the surfaces of other planets, and more. In that case you aren't just developing a propulsion system, you're also developing an entire space program to wrap around the propulsion system. That costs a lot of money. Even ignoring the other problems with the Orion technology, actually building (for example) one or more large exploration Orions in the 70s would cost substantially more than has ever been spent on any program of space exploration. The general point is that whatever you are building an Orion for, it's payload is not going to be cheap in absolute terms. You have to fill the ship up with thousands of tons of useful stuff in order for it to be worthwhile to build the ship in the first place. Building Orions is thus a de facto commitment to a large space program. Financially speaking, their launch cost advantages don't start to exist until you've already decided that what you want to do in space involves launching a substantial amount of stuff, and spending a substantial amount of money.

Next, there are secondary vehicles. One of the problems with the Orion propulsion system is that it cannot land. Once launched, it can come no closer than orbit to any planet. Using it to explore the solar systems thus requires a seperate means of getting to and from planets. Something which is, at a minimum, functionally equivalent to the lunar module (which could carry a crew of two to the surface of the moon along with minimal scientific equipment for a short stay, and then return to lunar orbit). An Orion planning serious exploration would need multiple landers, capable of carrying more stuff down to planets, supporting a longer stay, and preferably having more powerful engines to escape the gravity of bodies larger than the moon. While the Orion weight advantage allows a lot of landers to be carried, it wouldn't make them significantly cheaper. The landers themselves can't be built like battleships, because they have to be able to escape planetary gravity wells under their own chemical power. Development of the lunar lander was actually quite an expensive component of the Apollo program, and an Orion exploration program would tend to require even more expensive developments. We are talking about many billions of dollars in research, development, and production. Of course you can't really use the same lander for any arbitrary planet, as they have differing conditions, and you may need additional secondary vehicles to shuttle crew between Earth and the ship, and if desired to refuel it in Earth orbit.