basel switzerland

How are you getting to Basel? Car or train?
Basel is not car orientated. If you are driving you will need to park the car in paid parking and walk or catch a tram into the centre.
If you are arriving by train, there are two stations: Basel Badischer Bahnhof and Basel SBB, at opposite sides of the city, both equally convenient. If you are arriving from Germany your train will stop first at Badischer Bahnhof, and will either terminate their, or continue to Basel SBB.

Just get off at the Badischer Bahnhof. Walk outside, turn left. You need to buy a "Tageskarte" for public transport from the green machine. DO NOT BE AFRAID TO ASK, Baslers rarely eat tourists.
Problem: currently the tram line from there into the centre is being re-built, you need to take a shuttle bus (Tramersatz = tram replacement), for 2 stops then change to tram No. 6.

Get off the tram at Marktplatz. This is the city centre, with the big red town hall. There is a market every morning - currently lots of autumn fruit. Go into the town hall courtyard. Explore the surrounding streets.
Around the square is a labrinth of narrow lanes (no cars) which are worth exploring. I really like these. photo 1, photo 2.
End up at Münsterplatz (Cathedral Square) - (photo). Again do not be afraid to ask directions. I regularly have to give directions to lost tourists.
Go to the lookout at the back of the cathedral, take a ferry across the river (down the steps). Wlak along the far side of the river and enjoy the view back.

Lots of museums. Kunstmuseum (standard old masters). I prefer the Tinguely museum. 20th century art. Lots more.

ditto what Chris said. I pretty much did what he describes. I would add that there are many interesting fountains scattered around and for something different, somewhere (near the rathuis??) there was a huge mural of rock musicians.