It depends on what you mean by “cleaner” really. Is this a professional or amateur recording? If you just want to improve the recording, then there are many things you can try. EQing to get a better sound is probably the easiest. Stereo separation can be added or increased by using subtle stereo effects like chorus, delays and reverb or adding a slight distortion effect to the whole mix, then setting slightly different parameters for left and right. Remember that the lower frequencies are usually centred, and the higher frequencies are widened.
I've “restored” or improved bad cassette recordings. After the unwanted noise removal, I do things like split the spectrum up into four bands, adding relevant effects to each band and specialized stereo enhancement effects to the higher frequencies and reinforce and tighten the lower frequencies. In the end, I have about 15 stereo and mono tracks, with crazy routing between them. With this many tracks, you have to be well aware of phase issues and how to handle them. There's no reason you can't do this but on a smaller scale using Audacity. It depends on how much time you want to spend on it really.
There are many free vst plugins out there that you could use. They may not be as good as some of the specialized plugin suites, but you're only doing this for personal reasons.
Some simple things you can try is adding compression to the lower end to tighten it up, and adding some reverb to the top end to make it feel more spacey. You can then use EQ to bring out the frequencies you like and maybe enhance the midrange. Give it a try and see how it sounds. But if you have no clue what you are doing, you may find that you'll get lost pretty quickly and need to spend some time on it.