One of the best places to view the old city of Basel is from the far bank of the river Rhine. Cross over the historic Mittlere Brücke and walk down the promenade before returning on one of the river ferries. The Wild Maa ferry is a good option. If the river looks to rough then just walk back across the busy road bridge, Wettsteinbrücke and enjoy the views of Basel Cathedral.
Walk down the Rhine on the Kleinbasel side to Dreilandereck, or three country corner in English. The point where France, Germany and Switzerland actually meet is somewhere in the middle of the river, but there is a monument that looks a bit like a space craft gone wrong on the closest bit of land. Despite being in the middle of Basel's industrial area this is a really peaceful and pleasant spot and it's a nice walk to get to it. There is a restaurant here and boats heading up and down the river.
Where else can you hop between three countries in the space of a few seconds?!
Walking, boating, swiming, picnicing.
You can do a lot by the Rhein River,
it is not like East River in Manhattan...