Your question is awfully broad to expect helpful answers. But I guess if it were me, this is how I would approach it;
1) Make certain I liked my girlfriend A LOT!
2) Consider the convenience of a 3-month rail pass, but also consider learning a lot about the various rail discounts in each country and simply buying point-to-point tickets as you need them, Also consider busses, which are plentiful, cheap, and often just as fast as trains.
3) Find a reasonable flight to Lisbon. Work your way northeast through Spain and into France, then Belgium, Amsterdam, then central Germany, east to Czech, then south to Budapest (I know you didn't mention it, but you should have :), then west again through Austria (Vienna, Melk, Salzburg), then hop into southern Germany (Bavaria) for Munich & Fussen, then to Switzerland, then south into Italy.
4) At this point you either dump the girlfriend or ask her to marry you.
5) If you still have the time, energy and money to go on, take a boat across the Adriatic to Croatia, Greece & Turkey, (though personally, I would save that for another trip).
6) Fly a discount airline to London & see a bit of the UK, then home.
Generally speaking, I would try to alternate urban & rural visits, roughly 3 days each. Don't just hop from city to city. Without cleansing the palate with cute and calm rural visits, all cities will start to look the same.
Youth hostel beds will be plentiful at $25-$35 per person/night. In rural areas you may find some small hotels or B&B's that have comperably priced doubles. But in many places it will take more money than that for lodging unless you hostel.
If you avoid mid-upscale restaurants and only order hot food once a day, you can eat for $25/person/day. But try to go more upscale than that and you could blow your $100 on food alone.
Choose maybe one museum/castle/tourist site per day that requires you pay admission because that can add up fast. And after several weeks, you will grow weary of them.
