I studied in Rome for a few months and I was following a few different blogs about stuff free to do in Rome:
http://freeofchargeinrome.blogspot.de/
It had many times some interesting local events for free, or for under 5 bucks. There are also more touristy pages that, if you just google it, will tell you the 10 or 15 or X most fun free or cheap thing to do in the city of your choice.
Couchsurfing or youth hostel in the non-tourist seasons are also a very effective way of reducing the costs. So is not eating in the expensive food joints next to the monument, and filling a water bottle up whenever you can instead of paying 4 euros for a bottle of water in a restaurant!