There are lots of tours posted such as this one:

http://www.contiki.com/destinations/europe/tours/114-european-experience

(this is just an example, not necessarily what I'd want)

But I'm guessing it would be cheaper to just follow the path of the tour, use public transport, and book accommodation myself? Anyone have an idea of approximately how much cheaper it would be? Thanks in advance.

Just to clarify, most of the responses I've been getting are from people who are only available on weekends. I was kind of hoping for someone with a fairly long stretch of availability (like me), maybe a student on leave or something? The reason is that I was envisioning a big loop perhaps, starting and ending in Geneva, sort of like one of those tours, as opposed to going somewhere, and coming back to Geneva, then going somewhere else, etc.

Any tentative dates in mind ?

As a suggestion, you can do Amsterdam and London in a day. Basic stuff but you wont need hotels and easyjet tickets are cheap. i have done them both

As far as tentative dates, I'd want to start as soon as I can (but I still need to pack). Don't get me wrong, I like Geneva but I want to see other places too. Basically, the idea is that I've never been to Europe before, and I'm assuming I won't have a chance to return, so I want to see all the major stuff.

Some of the things that I need help with:

- which cities

- how many days in each city, what to do

- route/mode of transportation

- depending on the previous criteria, how long would it be expected to take? 

Do you use the hostels? Also, would it be better to take ground transportation, in order to see the scenery? 

Not at all. First easujet flight out from geneva airport in the morning, last flight back at night.

That gives you plenty of time to do the major stuff. In Amsterdam i had enough time to do the major museums and go for a boat trip before i had to go back. I took the train from the airport and just was on foot the whole time. i dont do space cakes or coffee shops so i dont know how those will affect you on time. 

As for London same thing to Gatwick airport and then use the tube to move around

Yes, a day is sufficient if you want to do it like a Chinese tourist who only has time to take a few pictures. In Amsterdam you can easily spend 3 days if you want to see things properly. However if she goes just for spacecake, then she can just bake some here herself, which is much cheaper and far less time consuming.

You are absolutely right. London needs a week even :) For a day trip you need to choose 2-3 things  and stick to that.

Thanks for the tips. The trip itself doesn't need to be that short, my availability is more or less open. It just would be nice to get started soon. Clearly, the spacecake comment was a joke, of course that's not the only reason for going.

I'm still looking for opportunities, you can send a private message. If you're planning to travel soon anyway and wouldn't mind a female companion to split costs. (lodging, and car if used) Especially if you're going to see the rest of Switzerland, or major cities in Italy, or maybe Paris and/or London. Everyone who's responded so far has already been to those places. 

Also, I'd appreciate people's opinions on the following: a tourist shouldn't leave Europe without seeing ____ (fill in the blank)