My husband and son and I are travelling to Rome arriving on 27th September 2008 rill 30th September 2008. Would like
to stay near the Colesseum, Vatican, Fountain of Trevi. Could you tell me if there is accomodation which is not too expensive
First, the three locations you mention are a bit dispersed, particularly the Vatican. Secondly, I don't know what you consider expensive. We found that everything in Italy was over $200, mostly over $250. This is for 3 star hotels. We stayed at the Residenza Cellini. It is near the train station and a decent walk to Trevi. It is a bit longer walk to the Forum. The subway goes from near Trevi to the Vatican. The price in April was 185euro. Rooms nice; breakfast wonderful. There is a refrigerator in the room and a market nearby so you can keep some food to save money. Fruits and vegetables are reasonable. Figure that the breakfast would cost at least 20 to 25euro per person if you ate in restaurants.
At this late date, you may have a challenge finding cheaper accomodation. If you stay in the area of Termini train station you will be relatively central to the Colosseum and Trevi Fountain, and in a cheaper area, but the Vatican is further away from most of the historic core of Rome.
Alternatively, to stay approximately between those three locations, you can consider the Pantheon neighborhood, which is a good deal more expensive.
I would suggest going to tripadvisor.com and reading the best-ranked hotels there. They also provide a rough estimate of the prices and let you search by price in dollars or euros.
Look at Cross pollinate.com for accommodations. They run the Beehive just two blocks from the Termini and have other places to rent also. Nice couple and The Beehive was nice/clean and close to trains and busses.