One would think that Thomas Jefferson's Town would feature Transportation to/from Monticello, but No!?????
Normally you can take the #1 bus (except on Sunday) to the popular two mile trail up the mountain. But Covid is still affecting service. You could also book a trip on a widespread para-transit, called JAUNT. Yeah, it's obviously a taxi/etc. situation. But that trail is super popular.
Closer to the station, I would start at the Dome Room of the Rotunda. From there you can feast your senses on the World Heritage Site of UVa's quad and imagine it open to the south. An equal distance the other way from the Amtrak station (both by free pseudo-trolley or a fifteen minute walk) is the Downtown Mall, one of the few successful ones, along with Boulder CO, from the 1970s. Kids like saying "downtown mall" for some reason. It's had a slight downturn lately, its ice park replaced by a tech office building.
But where you really want to go is Mel's Diner. Just up the (many) steps from the station. They are used to train people too. And musicians. I don't know, maybe ask them about the Crescent. It didn't become Amtrak until 1979. The Cardinal was saved by some Senatorial intervention. Different world now!
CVS is the third busiest station in VA. Washington and the NEC are the draw, for VA and NC. A train to Richmond would be successful, and the state bought the track, but it's at least ten years out.