Manchester, what do you intend to do there, visit Old Trafford?
Amsterdam is fine, the red-light district/rossebuurt is not tame like "geylang" for sure but it is worth visitng for its legends - mostly true according to one local guide. But of course, there are harmless things going on there. During the day, tourists admire at the narrow streets, architectures, river, etc
If you visit the Rossebuurt, just be careful not to take photos of the "occupied" windows.
Watch out for pickpockets and annoying people who want to sell you drugs or try to be funny/racist or try to chat with you.
Usually, have someone with you, if you do not want trouble. I mixed myself into a group of Jap tourists the last time someone followed me after making run of me racially. That guy is high and unpredictable, no use talking sense or all the police. Moreover, I was just passing through to get to Centraal.
If you want variety, visit Paris.
You take take the bullet train on the London-Amsterdam-Paris circuit.
http://www.fodors.com/community/europe/london-amsterdam-paris-9-days-things-not-to-miss.cfm
Summer is a good time to visit, and to look at women in summer clothings
