Hotel rooms tend to be small in Rome but there are some great options for families. Another option would be to rent an apartment during your stay. You can search on Airbnb and there are some fantastic options for families.
The Albergo Cesari Hotel
The Albergo Cesari Hotel is located between the Pantheon and the Trevi fountain. Family rooms are priced at €225 and up.
The Hotel Ponte Sisto
The Hotel Ponte Christo is another great option. It is central and has a beautiful courtyard and some of the rooms have terraces. The hotel is family friendly and cots are available on request.
The Grand Hotel del la Minerve
The Grand Hotel de la Minerve is located within the old city in the Piazza della Minerva. It is extremely central to all the sites and there are plenty of restaurants and cafes around it. The hotel was recently renovated. Rooms are very large and perfect for family travel and there are junior suites available which have a separate living room.
Hotel Santa Maria (Top Pick)
Hotel Santa Maria is a B&B set within the Trastevere district of Rome and offers a quiet, secluded haven away from the busy city. The hotel is set in a former convent in a busy neighborhood with plenty of restaurants and shops. It is set within a converted convent and the rooms are clustered around a courtyard filled with orange trees, there are 4 large suites that are ideal for parents with babies and toddlers.
The Westin Excelsior
The Westin Excelsior has an indoor, heated pool, jacuzzi, good sized rooms, and a fantastic location in the heart of Rome are what make the Westin a good choice for families. Its close to the Spanish Steps and Via Venato.