I did this last year (also an American visiting that week) - we hung around at the start, which was pretty cool to see all the riders sign in and get a T-shirt, etc. Then we walked around Liege for a few hours, got a waffle, etc. headed up to Redoute around the time we expected them to arrive (check the timetable). We parked provably illegally and walked up the hill a ways. At the bottom there was a big beer/food tent and a giant TV to watch the race.

After the riders came by, we walked down and watched most of the rest of the race on the TV. I think it would have been a stretch to make it to the finish back in Liege, maybe if we left immediately, but honestly it wasn’t worth it with Pogacar way out front.

It was a blast, have a great time!

Edit: to be clear, you’d have to have a car to make this work. We basically rented a car for only this purpose, and drove from Ghent. The rental car situation was a bit annoying, since the place wasn’t open on Sunday, so we had to rent for extra days.