Where to go for a weekend from Rome?

Dubrovnik? I think there flights between Rome and Dubrovnik. You could look at the budget airlines (easyjet, for example) and see where they fly to from Rome. In 2 hours it is possible to cover a lot of Europe by plane. Have you been to Corsica or Sardinia?

Thessaloniki and Bratislava are two of my favorite places that I traveled for a weekend, going through Ciampino airport. If you're interested I can provide more details, but I had a great time there! Cologne, Germany is great too - you can take the bus from Frankfurt-Hahn if you are flying Ryanair.

Also - I don't know if you've been to Istanbul yet, but Pegasus Air flies out of Fiumicino and while those flights are more expensive than Ryanair etc, once you get to Turkey it is very cheap!

If you are up for it, Turkey, Morocco, or Tunisia would be interesting and available with Budget flights. The solo female thing you would need to assess your own level of comfort. In Europe, Malta is often overlooked, maybe some of the lesser Greek isles. Chania on Crete is a great lesser visited town, you could probably find similar places in the Peloponnese.

Thanks for all of your responses! You've given me lots to think about...and research! Excited!

From Ciampino:
Ryanair flies to:
Alghero, Barcelona, Bari, Beauvais, Billund, Bergamo (ends 29 March 2014),[4] Bordeaux, Bratislava, Bremen, Brindisi, Budapest, Cagliari, Charleroi, Comiso/Ragusa, Dublin, Edinburgh, Eindhoven, Hahn, Karlsruhe/Baden-Baden, Kraków, London-Stansted, Madrid, Manchester, Marrakesh, Marseille, Moss, Porto, Santander, Seville, Stockholm–Skavsta, Thessaloniki, Trapani, Valencia, Vilnius, Warsaw-Modlin, Weeze, Wroclaw

Wizz Air flies to:
Bucharest, Cluj-Napoca, Chişinău, Katowice, Târgu Mureș, Timișoara

From Fiumicino:
EasyJet flies to:
Amsterdam, Athens, Basel/Mulhouse, Belgrade (begins 30 March 2014), Berlin-Schönefeld, Bristol, Copenhagen, Hamburg, London-Gatwick, Lyon, Madrid, Milan-Linate, Milan-Malpensa, Nantes (begins 1 April 2014),[6] Nice, Palermo, Paris-Orly, Prague (begins 30 March 2014),[6] Tel Aviv-Ben Gurion, Thessaloniki (begins 2 April 2014), Toulouse

Wizz Air flies to:
Budapest, Prague, Sofia, Vilnius, Warsaw-Chopin

Vueling AIrlines is coming into and out of FCO in a major way starting this spring.