It's important to do so at your current university. It has many advantages, as mentioned by the others, along with building a close work relationship with a professor. A relationship you'll have to maintain for the better part of 2-5 years during graduate study, depending on the length of study and type of degree you'll want.
Many "old school" techniques can be taught by the old farts at your university (don't call them that though
). I would suggest a more tenured, more prominent professor to do research with. They have strong reputations, are more willing to provide you with what you need, and most importantly, are
very willing to guide you.
Much of a student's creativity and application of chemical knowledge comes from experience with a professor at the undergraduate level.
Don't be afraid to come in on hours other than those scheduled, if your professor doesn't mind. My project is finished for this semester, but I will certainly come and visit during the summer and continue my work, since I'm already taking some summer classes anyway. Core curriculum...who needs it?