My wife and I like visiting Basel. A bit more laid back and less hectic than ZH.
I have a very good friend who lived and worked in Basel for 3 years. He was a single, gay man who had moved from NYC. He spent every weekend in either Zurich or London (not hard to get anywhere in Europe from Basel as has been mentioned). Living in Basel made his work life/commute easier and he had his weekends for partying and meeting people. Being single, he was free to make his weekend (and some week night) escapes - if you think that would be possible for you then it could be a good solution. If you don't think you would get away that often, you might consider choosing to live in Zurich.
I hope that helps. Have fun in Switzerland!
I would strongly recommend Basel. Find it more relaxed and open. Also, the daily commute from Zurich would be an issue. It takes at least 1 hr one way. The highway is jammed an trains are literally packed (you end up standing even with 1st class ticket).
Have you moved yet?
If your into skiiing/boarding Zurich is has better proximity to the mountains!