What on my car should I have looked at?

I drive a 2000 Chevrolet Blazer. For a little while now, it has been pulling to the side while driving at high speeds. It doesn't seem like it's pulling to any side specifically. Also, the floor seems to vibrate a little at high speeds. A friend of mine suggested that the u-joints had gone bad. Seems to be consistent with what I've looked up so far about bad u-joints. What should I do? Obviously safety is the first priority, but I am a college student looking to save money where I can.