This is the place I visited last year.

I agree with anna. If you really want a preposition, I think THAT is the best choice, i.e. This is the place that I visited last year. Choosing between WHICH or THAT is often confusing, even for native speakers. If you google 'which vs that' you should be able to find an explanation. In my opinion, WHERE sounds odd because PLACE already implies location. So, it's kind of redundant.