The road trip sounds fun to me! I would head down to I-40 and go west.
As I'm not looking at a map right now, I don't know the highway on the lower part of Illinois/Missouri but we went through there and stopped at Lincoln's cabin and then came down by St. Louis into Oklahoma City. If you stop in OKC, let me know as I know a great hotel/motel there. (2 day min from OKC to LA and that's pushing it).
OKC has the memorial right of the freeway. Nothing much until you get to Amarillo where it's the home of the 32 oz steak. (signs everywhere). Once you get into New Mexico, it's interesting as you have the red rock formations, the old adobe houses. Santa Fe is an off the highway trip but since you are on a timeline and have kids (assuming since you said Legoland), I don't know if smaller kids would enjoy Santa Fe as much as something else.
Arizona has the dinasours along the road, indian gift shops (along with N. Mexico). You will see a lot of Stuckeys (rest stop place) and buying one pecan log is a must. (I don't like them but I kept seeing them so had to buy one). We stopped at the Petrified Forest but wasn't too impressed. Since you are on a time line and budget, I'd save it for the Grand Canyon.
There are cheaper motels in Flagstaff and cheaper ones in Kingman. We stayed in Flagstaff and left early in the am to drive up to the Grand Canyon, we stayed there for about 6 hours and then drove back down and spent the night in Needles or Barstow (can't remember how far we made it that trip).
For time and $$, I'd be inclined to skip Vegas this time and perhaps go when it's an adult only trip. Sedona is nice but I'm thinking if your main goal is DL and the museum and LegoLand and looking for a few stops in between, I wouldn't veer that far off the regular highway.
You can find cheap lodging around DL. We use to stay across the street at Best Western but now stay a block away at Anaheim Plaza for $59 a night.
You could do your few days in DL, Legoland and then head up to San Francisco. I do day trips so not familiar with motels/hotels there.
From San Francisco, east on 80 towards Reno through Sacramento. From there, I do not know other than the national parks other's have mentioned. I haven't been past Reno on 80. (if anyone is a train buff, there is a nice train museum in Sacramento).
For the kids, research online for car games. Check books out of the library. If you have a DVD player etc. For two drivers, I don't think it would be that bad.
When we were transferred to OKC and traveled back to Sacramento yearly, sometimes we didn't have a lot of money. If you have AAA, Holiday Inn Express was good along I-40.
The months leading up to the trip, I bought a gift card to Shell and AM/PM and put some money on both so I could have gas cards. I bought the kids a disposible camera so they could take pictures along the way. I bought things at the store that I knew would last like peanut butter, peanut butter crackers, pringles.
We took an ice chest with milk/oj and a tupperware container to put sandwich meats, cheese in. I bought those 8 packs of single peanut butter cups and candy bars to put in that tupperware container in the ice chest for when the kids wanted a treat. We took cereals and I made muffins and cookies before we left. We stopped at rest stops and made sandwiches and had a soda from the ice chest. When we traveled to Michigan, Alabama, etc, I made it a point to stop at the larger truck stops for magnets of that state for my souvenirs which I now have in the photo album showing our trip with the photos. Cheap souvenirs. To change it up, bought salami, cheese and crackers and let the kids make their own little snacks.
It's doable if you treat it as an adventure. For our treats on the road, we'd stop at McD's or Wendys for one of their $1 ice creams.
I think I'm going to have to talk my bf into a driving trip up north to the east coast now.