I've done it twice now from Brandon, Manitoba. The first time it was just my teen daughters and I - we left at 4 am on a Friday morning and drove as far as Butte MT (stayed at Super 8 near the Interstate) the first night and the second night we made it to Barstow CA (stayed at a Days Inn there). The third day, we were in Anaheim and at Downtown Disney by 10 am. For the first 2 days I drove about 13 hours per day. Kids watched DVDs on their portable DVD player. We stopped lots (every 2 hours) and stretched our legs and saw some sagebrush....I must say that the interstate through Idaho and Utah is boring! Beautiful mountains in the distance though. We took a detour when going through Vegas and drove down the Strip - quite the scene at 7 pm for 2 prairie teens!
The second time my hubby and I did the drive and we drove right through from Manitoba to Vegas (a 24 hour drive) - while one of us drove, the other slept - this works well when you have 2 or more drivers. We got a really cheap hotel on the Strip (Imperial Palace) which we arranged on the road. We took a short walk to the Bellagio and saw the fountains but we were so beat we didn't see much else!

Then we coasted into Anaheim the next day and arrived around 1 or 2 pm.
Interstates were all good and there are plenty of hotels, restaurants and rest areas. There was one spot in Montana where you go through some pretty mountainous terrain (I think it was just east of Butte MT) but it was okay to drive it on the interstate - and on our returns, we tried to make sure we did that part of the drive during the day.
IMHO, I think we saved tons of money driving - compared to flying from any airport in Manitoba or Saskatchewan and then renting a car once there, the travel costs were much less and we were able to spend more money at Disney.

PM me if you'd like more specific info.