lets see, airline tickets to almost anywhere will cost around $700-1000, rental cars will depend on day or week so figure another $100 at a minimum. Hotels unless you motel 6 are going to cost $75 on up (we stopped once at a 'best western' near mono lake and it was $120 a night!) so those are some thing to think of, notice I did not include McD's at $8.00/meal x3 a day!
We just returned from 4500 mile trip. Cost $33/night at KOA's (7 nights), $20/ night at a state park, $20/night at a military campground (6 Days), rest of time we stayed on street or driveway of people we were visiting (14 days). Most I spent for gas at any one time was $150 in Ky. Got gas in chicago at 3.90 gal but had 1/2 tank so it was only $90.
Now to have alternates you can use a car and have the same costs, but fuel will be cheaper, CG's are also cheaper than motel 6's and unless you go to an unknown for cheaper. You can sleep in car (BTDT) but then must worry to find suitable comfort area for clean ups etc. and then unless like when I was a kid, (saw 1 couple doing this in Neb), cooking on camp stove in roadside rest area (my folks had a nash rambles SW so we slept in back, then dad would sleep while mom drove at night.
So can RV be expensive yes, but it is a wash IMO when you start looking at alternatives and maybe just a little cheaper depending on how you go. We are contemplating a quick trip to colo in oct, wife wants to go without the rv, so have fuel cost plus min of $100/night motel at destination for 3 days plus food!
Just figure out what you want. If you have an Rv of some sort or do you have to purchase and as noted costs will go from cheap for used (old RV) to $$ for new or newer. If old need to figure in costs to get ready which can accumulate rapidly depending on what is needed. Tires $12-1500 (6 or 7), any mech services required, Oil change at dealer for me is $60. If new figure costs per month in payments etc plus all of the above. If you have an rv the dmv cost will depend on your home location as will insurance and storage. If you have to purchase a TT or pickup what you want will also determine minimum costs. Many nice used private party sales on craigs list, just need to know what you are looking at to purchase.
Have fun whatever you decide to do.