Welcome. I've seen lots of discussions on forums on the topic of "which is cheaper, hotels or camper". I've seen the numbers massaged both ways. You also have to consider the intangible benefits - always in your own bed and bathroom, no bed bugs, etc.
Here's one point of reference. We recently priced out flying from MD to CA, hotels, rental car, eating out all the time vs. driving out with our camper. I literally threw out my notes last night but I just dug them out so I can give you my numbers.
Drive to San Francisco, 55 hours (5 1/2 days), 2850 miles.
300 gallons of gas, $900 one-way @$3/gallon (I assumed it would be back up by summer)
$100 for 2 nights at campsites (other nights at truck stops)
Then drive to Seattle, Chicago, MD over 3 weeks
4074 miles including side trips
428 gallons of gas, $1284
$800 for campsites @ $50 per night, 16 nights (5 at truck stops)
Normal home budget for food with most meals eat-in
$3084 total for a little over 4 weeks, not including attractions
Fly 3 of us one-way to San Francisco (my wife would fly in from a conference in FL so most of her flight cost would be covered so isn't counted here)
$700, cheapest option which includes a layover, I was conservative estimating fees/taxes.
Then drive to Seattle, Chicago, home over 3 weeks
$2100 hotels @ $100/night for 4 people
$1500 rental full-sized car for a month (tip - far cheaper than renting for 3 weeks!)
$1000 additional for food since all meals are eat-out
$5300 total for 3 weeks, not including attractions (and I think this is too low)
I also priced out a 3-week one-way rental of an RV from San Francisco to MD which was $7100 including one-way fee, daily fee @ $241/day, and mileage fees. This doesn't include airfare to CA, gas, campsite fees, etc.