euro2009, welcome to the Boards.
I don't think it will be necessary for you and your girlfriend to take an organised tour this time around as you have listed a variety of places that won't necessarily be covered by a tour and you'll still have to travel to those not on the tour. There's nothing wrong with a tour, but you seem to have given a good amount of thought to your itinerary already, so you have started the hard part.
As you're meeting your friend in Mykonos pretty much in the middle of your trip, you might have to adjust the order a little, but your thought of flying there is a good one. Based on your "wish list", you won't be able to fit everything in, as you're already aware, but perhaps this will work for you:
14 June arrive London - 2 days to start with then have time there at the end of your travels
16 June travel London - Luxembourg with BA (check their flights as they often offer special prices on this route). As has been mentioned, Ryanair have a 15kg checked luggage limit and fly from more remote airports, so only use them if there is no alternative. You could also take the Eurostar via Paris or Brussels and then continue on to Luxembourg, but the costs/time factor will be the same/more in this case.
16-19 June Luxembourg19 June travel Luxembourg - Paris the TGV you've looked at previously will be the best way, just in reverse order.
19-22 June Paris - this will allow a little more time to explore the city and as the train from Luxembourg is only 2hrs you'll have extra time on the day of arrival, especially if you leave around 10am from Lux.
22 June fly Paris - Mykonos via Athens: the most likey/suitable route for this will be to fly with EasyJet (
www.easyjet.com ) from Paris to Athens (from Orly Airport Paris to Athens main airport) then with Aegean Air from Athens to Mykonos (
www.aegeanair.gr ).
22-27 June Mykonos27 June (or 26th depending on plan) fly Mykonos to Venice (you may have to go via Athens depending on carriers and timetables).
27-29 June Venice29 June train Venice to Rome (fast train called Eurostar Italia takes just over 4hrs)
29 June - 3 July Rome - again this depends on your interests, but 4 days in Rome will allow you to see everything well. If you're not that interested, reduce it by one day.
3 July fly Rome - Barcelona - check Vueling (
www.vueling.com ) or Iberia Air (
www.iberia.com ) as they have good rates.
3-6 July Barcelona6 July Barcelona - Ibiza: check the flights and ferries for this route. Flights with Iberia or Spanair (think they are still flying) will take just over and hour, the fast ferry takes 4hr30.
6-9 July Ibiza: I realise this is one full day and two nights, but that should be plenty for you as it's not a cheap place to spend too much time.
9 July fly Ibiza to Madrid - check the Vueling website as they cover this route, as does EasyJet (I believe).
9-12 July Madrid: this is not a lot of time for Madrid, but you will still be able to see the city
12 July fly Madrid - Paris (EasyJet flies from Madrid to Orly airport which is Paris' 2nd airport)
12-15 July Paris: again, not a lot of time, but you'll still be able to explore a little.
15 July Paris to London: take the Eurostar as it's 2hrs20 central to central and if you book far enough in advance the tickets are a better price (3months out is good, no less than one month before travel).
15-17 July: London.
I realise this is more "rushed" than I'd usually recommend, and not all the cities on your wish list are covered, but as you see you simply don't have the time to see it all this time around. At least you can experience Summer in Europe and you're spending the bulk of your time in warmer areas, but that of course means crowds - and that's part of the Europe Summer experience!
Based on the above, you likely won't need to purchase a rail pass as you aren't spending that much time on trains that would be covered soley by a pass.
Booking hostels/accommodation for the Summer season is highly recommended - it's the busy period and it's not always possible to find accommodation at the last minute that will suit your needs and budget.
Is your girlfriend travelling with you at any stage? I ask as you're only spending 2 days in Luxembourg, which doesn't seem like a lot if you're visiting her there. If you're not (ie you're travelling alone) then 2 days is fine.
Adjust the suggested itinerary to suit your final plans, but it just gives you something to work with and an idea of how long travel can take between places. I'm sure the others will have more suggestions, and as long as you understand that you'd won't be able to see everything this time you'll still have a great trip.
. But I would spread out the days you can save by removing the second visit for some more time in Paris and Madrid (check the daytrips to Toledo/Segovia) and fly from here to London.