600 flavors of pee.
Just remembered something about Oklahoma. I don’t know if you can do this on any stretches of 66, but it is one of only a handful of states where you can legally drive on some of their highways at 90 mph (or is it 95?). I drove from Madison, WI to Tulsa a couple years ago and discovered this by accident.
I must be mis-remembering this, as I was looking at maps trying to figure out which road I was on, which I think was I 44, but everything I see says the speed limit is 75 on it. Which surprises me, because I remember being very surprised by the high limit when I saw it, but I’ve been on plenty of roads with a 70 mph limit, so it wouldn’t have been that big a deal. Maybe the traffic was moving at 90.
Another reminder – almost everybody speeds in the US on highways, normally somewhere between 5 and 15 mph over the limit. Don’t know how that compares to drivers in the UK.
If you take the Capitol Limited to Chicago, it stops in Harper’s Ferry, the small town where John Brown tried to start a slave rebellion in 1859. Unfortunately, the train probably won’t stop long enough for you to see much.
I-44’s speed limit is 75 MPH as of a couple of years ago. I use to drive it frequently when my daughter was going to a college in Texas. Of course you can probably get away with 5-10 mph over that limit…
You’ll find more affordable flights into Baltimore-Washington International airport (BWI) than into either of the ones closer to Washington DC itself. BWI isn’t that far away - 30ish miles north of Washington, I think (or maybe north of the Beltway, which is the highway that circles Washington).
Forgot to mention: at the Chicago end, consider Midway Airport (smaller, right in the city) and Milwaukee (Wisconsin) as alternatives to O’Hare for flights; those might offer cheaper alternatives. Milwaukee is quite a bit north (60 miles or so?? just guessing) but depending on where you want to go, it may be worth it.
Renting a car: yes, you certainly can pick up in Chicago and drop off in LA but there may be a stiff drop-off fee involved. Sometimes not; we’ve several times flown into LA and dropped a car off elsewhere (San Francisco and San Diego) and not been hit with a fee.
Hubby’s dream is to drive the length of Route 66 - the renewal of vows is a last minute decision when we saw how cheap it is to do in Vegas, seems a good way to celebrate 20 years of wedded bliss (mostly 
) We’ve got approx. 10 days to drive to Vegas which is around 180 miles or so a day so not too strenuous.
I think you can take a train or bus from BWI into downtown DC or Baltimore.
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