Absolutely! Do southern Europe and the Mediterranean. After Italy, you can EASILY make you're way to Greece, which is a country with as much history as Italy and might be even more beautiful!
I would take Eastern - it's more wild, unknown - but you can discover it. This part of continent is pure and not so full of tourists - as western - and there are many wonderful places ful of history. Go somewhere, where normally you wouldn't go.
To visit properly the old world (Europe) you have to visit:
Belgium (North) France (south) Italy (West) Greece (mainland) Spain (East) This the best of the best for a start.