not to give away my age, but i did italy and greece in college back in the winter of '96 with two friends. it was a great trip, and i too will be heading back before med school to check out more of europe.
i did eurail pass in italy, but in greece we took mostly buses and this worked out fine (we had been warned by a guidebook ahead of time that greece's train system was worse than its bus system). i forgot if we used railpass or just bought cheap ferry tix to go from brindisi, italy to larissa, greece. by the way, i highly recommend southern italy for its charm and friendlier, less tourist-weary people. i had the most off-the-beaten-path, "authentic" experience in brindisi (i don't doubt that there are more such experiences in asia, africa, and latin america, but if you're more into checking out western culture from the roots up (like i am) then europe comes first). i recommend italy in general if you like great cities. italy at the time was maybe a little cheaper than the u.s., and greece at the time was a good bit cheaper than both.
last i knew, flying into london is cheapest, but paris and frankfurt aren't too bad (it's also going to depend on where in the u.s. you're flying from). we got all tickets through
www.counciltravel.com. get an international student i.d. card and hostel card before you leave for discounts.
once there, i'm not sure about the suggestion to just take planes, as i believe travelling short distances is the rule in seeing europe and so i'm inclined to think you get your money's worth from eurail and buses. but it probably depends on how many cities and how far apart. eurail pass now covers ireland (and the ferry there).
$50 per day sounds just right to me. it's the max budget i'm planning on, so i expect to be under $50 on average. last time i went, we went to restaurants only occasionally. i ate a lot of bread and cheese from little grocery stores. hostels are not only cheaper than hotels, but highly recommended for the solo traveler. many folks from all over who are also going solo, and so instant friendships, exchange of information, and group outings abound. highly recommended. i went in the winter, when nothing needed to be booked in advance and everything was a bit cheaper. i would be reluctant about going into the bigger cities (paris, london, berlin, etc.) without a reservation in the height of summer.