I've spent weeks in London, a week in Barcelona and a day in Amsterdamage.
K. London:
I've always had connections there, so I have no idea about hotels/hostels, but I do know that they're among the priciest in Europe.
On the must-see tip, its hard to know where to even begin to begin. Leicester Square, Trafalgar Square, Piccadilly Circus, Green Park, Carnaby Street, Westminister Palace, Oxford Circus...all of these areas have cool shit going on during the day. But I often found the best places were off the beaten path, and just stumbled upon.
If you can spare a couple days for road trips, I really liked the college towns of Oxford and Cambridge. Same goes for cities in the periphery, like Brighton and Leeds.
Barcelona:
One of my favorite cities in the world. Just thinking of it gives me goosebumps. I think you'll be there around the time of the Sonar Festival, which is one of the most important electronic music festivals in the world.
I stayed at a place called Abegueil Hotel New York. Haha...I don't know how they got away with using the word hotel in their name, but anyway, total dive, but it was a shitload of fun. It's in this section of the city just away from Las Ramblas, to the East. Tiny streets, with lots of interesting shops selling food and wares. It's ghetto, but the place has a roof where all the kids go before the night out for wine drinking and chillin out under the Spanish moon.
Lots of people I met stayed at the Kabul - which is a party hostel if there ever was one. You've gotta book that one early, but word is that its fun fun fun.
Then there's the clubs! I found most of the places kinda cheesy, but I wasn't around long enough to get into the underground scene properly. The Black Sheep is the place for drunk German tourists and lots of cheap sangria. I met some key people who would later put me up in Germany on my trip while I was there.
Go down to the Olympic park complex. The architecture is jaw-dropping. Also, the waterfront of the Mediterranean is completely beach, since the restoration, and its sooo nice to just be there.....feels Carribean. All the women are topless and its a relaxed vibe. People walk around and sell you beer while you're lying there listening to your favorite tunes on the headphones. The swimming is great too, but I did see a condom float by one day.
Amsterdam:
I'll tell you my story from that place in person sometime. It was possibly the most fucked up day of my entire life.
But here's a hint, I wasn't able to score any place to sleep, cuz the city is a fucking chaotic mess of tourism in August. June is prolly much better...but its always quite busy. Book ahead in the major cities.
Wow, that was long-winded.
