I am overwhelmed by all the prompt, helpful information! Thanks so much for all the wonderful input. I'm off to the great websites you've recommended and I feel certain I will have some luck. You can really spend hours looking at hotel names and reading reviews, but it's information like this that is so helpful to get things narrowed down. Thanks again!

aahhh yes BUT reading reviews is key to becoming more efficient at your own research abilities!

I was 22 when I went to Rome by myself. I stayed at the Hotel des Artistes. It was safe. It is a normal hotel but there is one floor that serves as a mini-hostel. I stayed there and met some other really nice girls from all over. It was by far the nicest hostel I stayed at during my European travels. http://www.hoteldesartistes.com/lodging-in-rome.html.. It cost $25 euros.
The normal hotel rooms are about 75-80 euros... it sounds like their budget is a bit more-- but they could then spring for some nicer meals..

I can highly recommend the Nicolas Inn B&B. Five of us stayed there in late May. We had a double and a triple; the triple was 140 euros and the double was 120 euros (at that time).

The owners are a really nice young American woman, Melissa, and her Italian/French/Lebanese husband Francois. They are incredibly helpful.

The location is good, just a few minutes walk to the Forum, the breakfast fantastic, the rooms very nice (contemporary decor) and there is an inexpensive and good trattoria right next door.

I would definitely stay there again.

We stayed at Hotel Aberdeen
http://www.travel.it/roma/aberdeen/
for 88 € a night last November. We thought it was a great hotel -- friendly and helpful staff, convenient location, reasonably quiet street, and very safe (right across the street from the Ministry of Defense). It may be a bit late to get in there though, as it's recommended by Rick Steves (he actually had a tour group there when we were there) and I think books up pretty early.

My 18-year old daughter and three friends stayed at the Alessandro Palace Youth Hostel this summer and thought it was great. Cost for adouble with bath is 70 euro. It's just a 5 minute safe walk from Termini. http://www.hostelalessandropalace.com/

Wonderful info! I've sent out serveral requests and am waiting for availability responses. Since you guys have been so helpful, could I be so greedy as to ask for some other great recommendations for the same criteria in Milan,Venice and Florence? Right now they are booked at Gran Duca di York in Milan, still looking for Venice, and Hotel Pendini in Florence. Any feedback?

In Florence last March, I stayed at the Residenza Johanna I and liked it very much. It is modest and rooms are small, but it is attractively furnished and in a safe area on the north side of the Centro Storico. A double is 80-95 euro. http://www.johanna.it/Len/johanna1.html

In Venice -- try this B&B:
Ca'turelli
They can read about it and book it on the veniceby.com website.

I think our triple in May was 120 euros so a double will be less. Nice place and great location.

Here is another idea for Rome. There is a hostel run by a women's organization, just for women, in the Trastevere nieghborhood, which has lots of cafes, music venues, artists, etc. They have all types of rooms, both dorm style and more private (like singles/doubles, etc) w/ and w/o bath. They have a cafe, yoga classes, a garden, etc.

It is called Fosteria Orsa Maggiore and the rather cumbersome email is:
casainternazionaledelledonne

The website has info on the organization but also specifically on the lodging. It is not a convent-type hostel, so I believe there is no curfew.
It sounds more like a cool hotel for women.

I didn't stay there because one of our group was a guy, but I thought it looked interesting. The only problem was that you had to reserve with a bank deposit, they don't take credit cards. If you do a search under the name "orsa maggiore" on this site, I think you will find some past posts and a discussion about making the deposit.

I first read about it in the Lonely Planet Italy guidebook (which I would recommend to your daughter anyway) so they can read about it...

http://www.hoteldesartistes.com
i can second this recommendation. i stayed there from 10-12 sept 2005 with my hubby & 10 yr old in the hotel part.basically the hotel rooms are more expensive than the hostel accom but they share the same breakfast room, reception etc - they are just on different floors.it is really convenient to termini station -but on the nicer side - also they give you discount cards for 2 restaurants in the next street, both good. reception is staffed 24 hrs, they are really helpful & speak english & it is secure. also has a great roof terrace for early evening drinks/breakfast/coffee/sunbathing/meeting others.

Cliquot1:
In Venice the hotels most frequently recommended on Fodors are La Calcina and Locanda Orseolo. The Orseolo, especially, is cited for the exceptional hospitality of its hosts. If they have availability, it's probably the kind of place I'd like looking after my girls.

They're both very popular, so they may not have anything to offer.

http://www.locandaorseolo.com
http://www.lacalcina.com/

in venice last year we booked last minute & could not find anything at all!! we ended up on the lido for a couple of days, staying at a place called villa albertina http://www.villalbertina.com/
there are vaparetto into central venice from real early am until v. late pm and it doesn't take long - 20 mins. in the end it was really graet staying on the lido as eating out was cheaper than central venice , as was the hotel. also , it had areally nice family vibe to it - v. safe going out at night etc. i would go back again as the room was great value & a nice place to go