I visited Cinque Terre in late June with no reservations and on a cheap budget. I stayed in Vernazza the first night in a room that a family was renting; if you look at map of Vernazza when you get in off the Eurail, there are people watching who will offer you lodging (for a fee, of course). I assume it’s that way with a lot of the cities as it seems everyone has a room to let.
The tourist office will also provide you with a list of people and inns to try. I wouldn’t recommend staying in Monterosso unless you’re looking for a hotel, as it’s very touristy. People who’ve stayed in the hostel at Manarola have loved it. I don’t know if you’d need a reservation (it can’t hurt), but I managed to get a room without reservations during the peak tourist season.
All of the five towns are stunning and unique. Of the cities, Vernazza is the one that stars in the guidebook and postcard pictures, though it’s tiny. Monterosso has the beaches. Manarola was absolutely lovely. The hike between the cities is worth it, but do NOT wear sandals- i figured this out the hard way.