"I don't agree with you about Paris being expensive."

I don't know how you define expensive but I'm sure that Prague or Berlin are considerable cheaper.

One can visit fairly inexpensive at most places but for me it's a heck of a lot more fun if can walk into most of the places without busting my budget instead of needing to plan ahead.

Now, if they really want to go to Paris and London, sure go there and plan ahead to safe some money.

But if they don't really care about Paris and London but just want to go to some European city, then there might be better destinations since the cheaper price level offers options you don't get in expensive cities for the same price.

You may like to consider Busabout - it offers the security of being with a group (if you want) AND the flexibility to do your own thing too (if you prefer).

There's some good information in the FAQs - comparing their service with rail passes, how they can help you book hostels etc...

Obviously it's not for everyone - but maybe worth a look?

http://www.busabout.com/faqs

I'm not an expert on 18 year olds, other than I was one once...so in my experience, traveling aged 18 was heavily weighted towards the social experience rather than lengthy stays in each location.

I'd be pretty happy to think that an 18 year old was experiencing different cultures, flexing their passport, and seeing that people live differently in other parts of the world, and would be less worried about how long they spent in each location or how many churches and museums they see. Personally, at 18 I'd go for more places and less time...assuming that the budget allows...and that they would cope with the logistics.

There are many places I visited as a young traveller (for..ssshhh....a day or two) that I've returned to since - with more money to spend and more time to linger and different interests, and as a result had a totally different experience. Traveling is pretty cool like that!

In Amsterdam check out Stayokay: it's a revamp of the youth hostel associaton, and in Amsterdam centre they have two hostels: one in Vondelpark, and one on Kloveniersgracht. Book ahead for their private rooms. I've stayed at the one in Vondelpark and it's excellent. Bonus: they'll be meeting fellow travelers, so it's easy to connect to people to do things together. Staff are excellent and super helpful.

4 days in Amsterdam is easy to fill. Museums, don't know, but Amsterdam has a vibrant and safe cultural scene and there's lots to do

http://www.spottedbylocals.com/amsterdam/
http://www.stayokay.com/en/hostel/amsterdam-vondelpark

Two weeks isn't very long.
Given that they have years of travel before them, and Rome, Amsterdam etc. are not going away (we hope), I'd suggest checking into a fairly central hostel in London. They will find loads of things to do there, especially if they make friends with other young people. If they like, they could hop on a bus and see other bits of the UK, but I think that London would keep them busy for a week.
Starting in the UK would acclimatise them to being abroad but without a language problem
After a week in London, they could then take the Eurostar to Paris.
There, if the impulse overtook them, they could visit another city, possibly on an overnight train. The Man in Seat 61 is an excellent resource.
http://www.seat61.com/
His instructions are very detailed, practically like being led by the hand.

I like the premise of what Miss Prism suggested--getting acclimated, making some contacts, and then continuing on to another venue--day trips in the UK and then somewhere else for a stay perhaps with day trips.
And when choosing "cheaper alternatives" don't forget the cost of getting to them.
An open jaw flight would also be preferable.
Budget??? Even a per diem would help--and then the $1000 airfare cost (probably).

Everyone in Amsterdam speaks English. It's not as if they would have to speak or learn a language other than English to do anything there. Unlike Paris, I might add.

Have them plan on taking an organized day tour in each of the cities. That costs some money but gives the highlights of each city. Hop On Hop Off buses are an alternative.

I like to plan on 2 activities per day - one in the morning and one in the afternoon along with other 'would be nice if we have the time' activities. Don't over schedule.

Get them involved in planning. Although I didn't plan an European vacation until I was 20, I did plan one for the Caribbean when I was 17. Both were successes if I do say myself! And both were primarily planned using Fodor's books back in the dark ages.

I think we may have lost the OP . . .