Rome has it's fair share of hostels around town. You can book ahead of time, or it is possible to find a place once you arrive if it isn't a busy time of year. The important thing to consider is whether you actually want to stay at a hostel or a hotel. In Europe, if you're traveling as a couple, a cheap hotel room can often be cheaper than two beds in a dorm. You'll have your privacy and the comforts of a simple hotel room. You won't have a kitchen, which you'll likely to have in a hostel. You also won't have the ready made group of friends that often comes with a hostel. A hotel is likely, although not definitely, to be cleaner. It's a difficult decision, but if you're traveling in a couple, it's almost always a little better to go with a hotel room, and skip the hostel. It's a different ambiance, but sometimes that difference is much appreciated, especially if you've been traveling for a long time.