[I got this idea of sharing some of my experiences, good and bad, in my job-hunting so other people don't have to make the same mistakes as I did. I hope the information will be useful for you, and you can comment to share your own should you want to.]
After I graduated last year, I got so confused between two geographical job-hunting strategies. One, I could relocate to a particular city and search for jobs there directly or - Two, I could search indirectly without relocating first. Obviously each has its own pros and cons. I chose the latter, and switched to the first only recently. I asked a lot of people for their opinion, and they almost evenly split in recommending one over the other to me. Since I did both, I knew which one is working and which one is not, at least in my case.
With the second choice, I could save money since I lived in a small city and there was less pressure in my part because I could stretch my saving for a longer period. Searching indirectly is very much doable by using the Internet. This option is obvious if I didn't have any preference to a particular city. Even though I do have a preference (if it's not apparent to you yet, I'm writing from DC), there were several reasons which prevented me from opting with the first choice from the get-go. Everyone situation is unique, and I think in most cases, they would choose the second option.
With the first choice, I hardly know anybody living in the new city at that time, and I was opening my option too wide by considering other places such as Chicago, Boston, Philadelphia, and Seattle. Clearly, there would be much pressure in my part since I could only stretch my saving for much lesser period. Unless you already received a job offer while you are still in college, the first option is the way to go, in my opinion. Recent grads will be hard-pressed in finding a job with relocation benefit since most positions open for them are entry-level. Plus, relocating will open other channels which were not available previously such as networking, classified ads, and temping.
In hindsight, I should have made the decision to relocate earlier. I realized that it'd be difficult to decide it immediately, but I should have given myself a timeframe which I had to adhere (say within three months or otherwise relocate after that period is reached). So, if you just graduate or will be graduating in the near future, consider relocation seriously and make necessary preparations so the decision can be made in a timely manner. The shorter you are out of job, the less psychological (and financial) pressure you will face.