general question about accomodations

Depends entirely on where and when. If you post your itinerary some people might have a better idea. I used to not book ahead, but since I need singles, which are in short supply, these days I almost always book ahead - I enjoy the planning process and it saves hassle (less hassle if you can park someone in a cafe with the bags).

I don't know what TI means but here is what we do. Determine what city you want to start your trip. DO RESEARCH both online and using guidebooks. We use Rugh Guides. Do a Google seach on the city you will be landing at: Istanbul, hotels. You will be able to find more hotels than you need. If you are staying more thant three or four days the hotel may be able to pick you up at the airport. We have done this twice having made our own reservations at Best Western hotels. Don't hesitate to correspond directly with the hotel using email. You will probably get a better deal this way. We have. We use trains and when we get to a city we want to stay at we get off, ask someone at the ticket counter or visitors information where the information office is for visitors. People there are more than helpful. We have reservations at the beginning and end of each trip that we make directly with the hotels. You can find the proximity of a hotel to the reail station online. Once we are on the ground and through the first city we have no reservations until we get to where we want to go next. Only once did we find all the hotels filled up - with musicians for a jazz fest. I would say travel with confidence that everything will turn out all right, because it usually does.

How can you be sure that each train station you arrive at will even have a TI? But if a TI is available, most that I've seen in Europe will help you secure accomodations.

I'd also like to add that sometimes it'll be more difficult during peak tourist seasons, so time of year should be taken into consideration, and you may want to familiarize yourself with any big festivals/conventions that might be going on in the towns around the time you want to visit. For instance (and these are only examples because they are clearly not in Eastern Europe), showing up in Munich during Oktoberfest or London during the Olympics might significantly reduce your lodging options/price ranges. Out of curiosity, which countries/areas are you thinking about, and at what time of year?

TI = Tourist Information Office (bureau, centre, etc.) Most used to be government run in Europe, many now privately run or on a concession. Some few are just advertising booking offices for a particular company or group.

to budapest you should be ok, there are plenty people with signs at the train station with rooms. other cities are not so common, so you're better off with a guidebook so you know where to go.

TIs Usually are different than an information desk in a train station. We have asked at the train stations where the Tourist Information Office is, and are told to go to so and so. The TIs we have used are near "downtown" and have given us enourmous help in finding a hotel. That's all we have used them for although we prowl around all the information kiosks to see if they have something interesting.

TI's may not be open when you arrive. Are you traveling by train and saddled with your luggage? Or renting a car and unemcumbered. If you aren't limited by price, you will probably be okay. Also depends on the time of year. Lots of European tourists in Europe in the summer . . . I like to check out the hotels online, compare prices (sometimes one website has a significantly lower price on the same rooms as other sites) and read the reviews (with some skepticism). Rooms at similar prices in similar locations can have widely varying standards. But I stay in larger cities.