First trip to Europe! Right after College

You said France but didn't specify where - I am assuming you're thinking of Paris, which would be a great spot for you - tons to see!

One way your routing would work like this: Paris, train to Amsterdam, train to Berlin, train to Prague. You might want to sneak Vienna in there between Prague and Budapest because it breaks up a long train ride and it's worth stopping there. From Budapest, you're left with Italy, looking at your list. I think I'd fly that route as the train is long...the rest of the train connections (above) are not bad. Pick a city in the south of Italy (for warmer temps) and work your way north.

As to Barcelona -you could work it in. Start there before Paris and then train up to Paris and go from there. Barcelona will be one of your WARMEST cities in February, but everything will be chilly that time of year. The average high in Berlin in February is 39!

After Budapest, any where to go before Italy? I'm wide open for suggestions.

Also for BCN - I was thinking to go there towards the end of the trip (march) when it would be hotter. Is that a good move?

I'd suggest the following routing over 8 weeks with 3-5 nights at each destination.
Barcelona - 5
Avignon (Provence) - 3
Nice (Cote d'Azur) - 3
Milan - 2
Venice - 3
Florence - 3
Rome - 4
Fly to Budapest - 5
Vienna (??) - 3
Prague - 5
Berlin - 5
Amsterdam - 5
Paris - 5
London (??) - 5

Love this list!

Would you recommend each destination in the order you listed? I'm coming from the US.

Mardi Gras will be Feburary 28 next year, and Carnival is celebrated well in several areas; this is my particular favorite, north of Torino: http://www.storicocarnevaleivrea.it/English/.

Yes, by train in that order, except the one flight from Rome to Budapest. Start in the south in February and finish in the north in March. It will be quite wintery throughout.

Can I fit in Croatia and Bratislava along the way?

Train connections are not particularly quick and convenient to Croatia. There are a few ferries from Italy (e.g., Ancona-Split), but less frequent in winter, as well as flights from Rome. How to Look Up Train Schedules and Routes Online gives you the DB train schedule link and tips for using it. For the flights you may need, try www.skyscanner.com.

Bratislava, I'm sure is a wonderful place, but does not feature highly on any 'must do' lists.
Croatia adds difficult logistics (few flights, slow trains) and late winter is not the preferred time to visit.

I'm cool with not going to Croatia if it makes everything difficult. I'm open to anywhere that makes sense logistical

Are you traveling alone? Why this time of year? Daylight hours will not be long. You say 4-8 weeks. What is a more definitive time frame? At this time of year I would choose big cities and spend a MINIMUM of 4 nights which will give you a MINIMUM of 3 days (depending upon transportation between locations, checking in to lodgings, etc). April would be a more favorable time of year but maybe that doesn't work.

Yes, I will be traveling solo. I'm going this time of year because it is right after school, and before I start working. When I say 4-8 weeks: I have up to 8 weeks (including first week of April), and will probably go for 6 weeks, but I do have flexibility to go longer if necessary.

If you are going to Budapest and Italy, I would definitely recommend stopping in Slovenia on the way. I traveled solo there a couple years ago. It's such an underrated country! Ljubljana is a great city and the mountain scenery is incredible. It also has cool coastal cities that look like what you would picture Italy to be (actually some of them used to belong to Italy). From Piran, Slovenia you can take a quick 30 minute ferry to Italy and go from there.