Calw Old Town

The city is really pretty, in some places, if it weren't for the crazy drivers...

Calw is just... Calw - as a local, my opinion is probably distorted, but tourists love the charm of the "small town pearl" with its pretty old town. There are plenty of places to stop for a bite to eat. My favorites for coffee and cake are Café Goldmund, Café am Markt and Caféhäusle, but the other alternatives aren't bad either.
Fruit and Turkish sweets are available at Kaya on Badstrasse, which also accepts card payments.
On suitability for racing bikes: The paved pedestrian zone (from Lederstrasse to Badstrasse) does allow bicycles, but only at walking pace. This should definitely be adhered to out of consideration for everyone - especially on a summer weekend when it's particularly busy!
If you want to speed, you should take Bischofsstrasse and Bahnhofstrasse. You can easily go with the flow of traffic there at 30-40km/h, although in the worst case scenario there will be several traffic lights waiting for you.