It is difficult to fly over and back to Europe for less than $500, even if you go stand-by and live on the East Coast. However, cheap tickets from consolidators now approach the price of a stand-by ticket (if you can find one), so spending $600 to $1,000 is realistic. Do not forget that travel agents can still save you headaches as well as money.
Plan on spending $300 a day for a nice hotel room, three meals in a restaurant, daytime touring activities and a show at night. This price comes down a bit if you are traveling with a partner, who can split the cost of a room.
With a little research, a nice room can be had even in Paris for less than 50 Euros. (Research the major guidebooks to find where the cheaper rooms are). Enjoy a nice dinner at a restaurant, a day at the museum and only to go to a show every other night for $100 a day.
Stay at a youth hostel and eat most meals at the Markets; you can get your daily rate down to around $50 a night. A hostel bed still will cost you about $20 to $30 a night. If you travel with a partner, a shared room makes just as much sense. Do not forget that hostels sometimes have private rooms for rent or they can find you a place in town for a comparable price.
Bring a touring bike and tent and watch your daily price drop even more. In some places, you may be able to find free spots to pitch a tent, but your best bet is to stay at campgrounds. Still, you might want to hit a hostel every now and then, especially if the weather turns bad.