I would suggest that she start with rough guide / lonely planet guides, then check the specific hostels one more than one site - www.hostels.com
and TripAdvisor. One she narrows it down to one or two, she can post specific questions in the relevant forums on trip advisor about things such as whether the area is generally a safe one, how far to he nearest station etc.
If you read reviews look for patterns - if one person says that the place was dirty, it may be that they are overly picky, or had a bad day. If lots of people say the same then it's probably correct.
Rome has some women-only hostels, if she would feel safer with that than a mixed one. There are also quite a lot of hostels in Rome which are run by various religious orders or groups. They don't (generally) have any restrictions about who can stay, but are likely to be a lot quieter and probably attract an older clientele, which again, may feel safer.
It's worth thinking about what she wants to do, what her priorities are etc - for instance, larger hostels will have more facilities, may well organize or facilitate trips and other activities, but are often very noisy, and can be less secure due to the numbers of people going in and out. Smaller hostels are likely to be much quieter, generally less likely to attract big groups of be the focus of boozy parties, but are less likely to have extra facilities.
form what I recall, a lot of hostels (and cheap hotels) are in the Termini area, near the main railway station (and in walking distance of most of the big attractions) This area has a bit of a bad reputation but no more so than any city centre, but if your daughter is concerned than she might want to look for hostels which are on a fairly main road, rather than down back streets - they'll be noisy, but the main streets are well lit and public transport is good.
When I travelled alone and stayed in hostels, i would normally choose to stay either in a single room, or a medium sized dorm (4-6 people) for preference - sharing a 2-bed dorm with a stranger felt less safe to me than being in a larger room. That said, the only trouble I ever had was with noise/disruption (we booked late, and ended up in a big (12 person) dorm in a big hostel in Barcelona - there were several big groups (stags and hens) who were out late and drinking heavily every night, and of course very loud and clumsy when they came to the dorm.)
Generally, however, I've had very good experiences - met lots of interesting people, and generally found people to be very welcoming at to a great extent to look out for one another (I got acute food poisoning when I was in Warsaw, and the kindness and help of the other guests and the staff was amazing)
I hope she has fantastic time!