When planning a trip I start with a general itinerary and with your wants I would work on a route from Ohio to Montana and Yellowstone and then south to either Salt Lake City and cut across to SF bay area or go further south on I-15 to Las Vegas and then head across to Goleta going through Tehachapi, CA rather than the LA basin. Going through Tehachapi to Paso Robles will put you on Hwy 101 north of Goleta and in the heart of the central California wine country.
I then use Google maps to determine the approximate mileage and in your case from your home town to Yellowstone, Yellowstone to Salt Lake City, Salt Lake City to Tehachapi, and Tehachapi to Goleta. I would guess that the total distance covered will be close to 3,000 miles. Round trip you would be driving 6000 miles. At an average speed of 55 MPH (allowing for rest stops, gas, meals) that would be 109 hours of driving at a minimum.
If you have 21 days for the trip you will be spending an average of 5 hours a day driving which is not going to be fun for you or your passengers. The difficult part is traversing the country.
An alternative is to fly to not try to go by RV from your home but instead rent an RV in Bozeman or Boise for Yellowstone and Grand Tetons, and then flying to San Francisco and renting an RV there and driving it south to Goleta. You give up 3 days with air travel but that is better than the 3,000 miles and 6-8 days of cross country travel to get to the western USA from Ohio.
Once I have a manageable trip laid out I next look at where I want to stay along the way and where I can get diesel and where I can find dump stations.
Consider changing your plans and visit Tahoe, Yosemite, Mineral King, the Pacific Coast and the central coastal areas from Monterey, Morro Bay, "SLO country" to Goleta. There are RV rentals available in the San Francisco area of Class C and B and B+ motorhomes.
Even living in northern California it is nearly a 3,000 mile journey for us to go to Yellowstone and I would not try to combine it with a segment going through Goleta/Santa Barbara on one trip unless I had a couple months to travel.
