[Cut to the chase and see some useful Ulm links now]
You probably will arrive in Ulm by train, that´s of course the most popular way to get anywhere in Germany. From the Ulm main station (Hauptbahnhof) you won´t see much. Just a McDonalds, which locals say it was the former Einstein´s house (although he was born there but only 11 months later his parents moved away to Munique). You get to see also the Strassenbahn bustop (german word for that is Haltestelle) where you can take your bus or tram to whatever accomodation you booked. By the way, to see all bus schedules in nice pdf format just click on the url below:
After setting up, you will be ready for a short walk. My suggestion is just to go back to the main station, cross the street and try to find your way through the Bahnhofstrasse (it is just behind the McDonalds). If you look carefully you will notice a small Einstein´s statue. By the way, Strasse in German means street.
At the Bahnhofstrasse you will find the main commercial zone of Ulm. Many places to eat, stores, including two bookstores of reasonable size (books in English are available). If it is springtime, you might be up for a coffee or a UR-Weizen beer (strong typical german beer).
From 5 to 10 minutes going up this way, you are binded to see the ULM MÜNSTER. The highest cathedral in Europe. See some photos now just in case you get lost. Arriving in the Münster you are right at the heart of the city, in the center of the old city (Altestadt) as well.
Take your time at Münster Square (Münster Platz). Maybe you can even make some fotos of the nice birds sculptures half buried in the sand, or you can just circunavigate the Cathedral noticing the many stores, restaurants and even a Deutsche Bank surrounding it.
From the Münster you will be ready to explore the nicest part of Ulm: Fischermannsviertel.