Café Florian
Marktplatz 8
(http://www.cafe-florian.de/) beer, wine and small sancks on the markplatz, tapas is a specialty here.
Woinemer Hausbrauerei
The Woinemer Hausbrauerei (http://www.woinemer-hausb...), Friedrichstr. 23, Micro brewery with a beer garden, also serve hearty German meals. Their beer is only availible in Weinheim - you can also buy it at local super markets, maybe as a souvenir.
Windeck castle
In the summer, enjoy a beer or an apple cider and a spectacular view across the town and the rhine valley in the beer garden in the ruins of castle windeck, up the hill in the east of the town. (http://www.rohewo.de/burg...) you'll definitely be ready for a beer after the walk up. open tuesdays to sundays in fine weather from 5pm, and on sundays and public holidays from 10am.