Everyone has made some great points.
Average walking speed is 2.5 to 3 mph.
That makes it a 23 hour round trip, before you include the trip on the transport and the time spent in the museum etc.
Can you stay somewhere overnight before heading home the next day?
Have they offered you a lift in exchange for petrol/gas money?

Does your friend even realise you would have to walk 12 hrs just to reach public transport, and depending where you live put your safety at risk?
If they do this is an absurd request, and I would strongly question their motivations, especially if they are fortunate enough to drive themselves.

I would say this isn't wether it's worth it, it's wether it practical and safe.

Here's hoping you manage to work something out.