I'd go early if it's the last night in that city. I hung out along with some other Coldplayers after the July 9th show in DC. Despite security saying don't bother we stayed.
Then later another security person told us since it was their final night in the city they left straight away and caught the last British Airways flight from Dulles to Heathrow. She seemed pretty tuned in and was actually pretty nice and gave us some details of how they do a runner at the venue. She claimed the band never sticks around but I knew that wasn't true having read about people meeting them after some shows.
She told us the band had family in town and they went to a sushi place near Verizon Center after the first show on the 8th, had a big party to celebrate their upcoming break and didn't go back to the hotel until around 4:00AM.
She said they stayed at Hotel Monaco which is a small boutique hotel right down the street from Verizon Center. Just in case we hung around longer until one of the roadies came up and said they left so I did too. Of course he could have been lying in which case I'll curl up into a ball and die!