If you are taking the train, you are limited in where you can go upon arrival. You will be pretty well stuck in the falls area. However, there is a local bus (WEGO, see below) that goes to Niagara on the Lake if you are interested (and it is a nice area).
The GO train runs weekends in the summer, no advance purchase required. There is the local WEGO bus that services the Falls. You can find more info and links here:
http://gotransit.com/public/en/travelling/niagara.aspx
VIA will require advance purchase. Not sure of the their service.
http://www.viarail.ca/