Ciao Marian,
Since you have just 3 nights between Venice and Rome, I'd say the best place to stay in is in Florence and to use trains for transportation, they are very reliable and easy to use.
You do need to be at the airport at least 2 hours before, but trains luckily have gotten faster and Florence-Rome takes about 1.5 hours... add to that the train shuttle to the airport, but I think it is doable the day of.... so you could leave Florence around 9am to be in Rome Termini by 10.30 or 11 at the latest, have time to catch the train to the airport and make it on time... you can check train schedules on both http://www.trenitalia.com/ and http://www.italotreno.it/en/ to see schedules and cost as there are specials often. On Trenitalia, make sure to take the Frecciarossa or Frecciargento, those are the fast trains.... the slow regional ones take about 3.5 hours, you definitely do not want to take one of those.
As far as accommodation in Florence, I'd recommend a B&B or small hotel in the center of the city so that you're easy walking distance from all of the sights. You can go out, and go back to rest as many times as you want... take time to enjoy meals and soak in the setting and atmosphere, Italy is magicalI am sure if you love it and can, you'll come back again!
You can find some very nice B&Bs on this page: http://www.florenceaccommodation.com...nd-breakfasts/
It is hard to recommend one in particular without knowing your budget but take a look and ask any more questions and I'll try to help!
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