traveling in Italy

there are bus connections/services like Flixbus at very interesting budget but train connections are much faster so you wont waste time in road traffic. Trenitalia and Italo train companies offer various low cost solutions If booked well ahead.

Where are you wanting to travel? We could probably give better recommendations if we knew which cities are involved in Italy.

This is a rather vague question. If 3 days is all you have, I recommend staying in one hotel in one area and just enjoying your time there. Some cities are more expensive for hotels than others.

By foot and public transport (buses, trains, etc), and staying in hostels or monastery stays

michelle,

I agree with previous replies. Your question is rather vague and it would help if you could provide more information on where in Italy you'll be travelling. Trains are usually one of the best and most efficient methods of getting around Italy.