The workplace will depend on the specific type of company the designer is working for. A web design company tends to be part of the creative industries and will typically have a contemporary approach to office space. These kinds of companies often employ ideas thought to enhance the creative process and aim to create open offices where ideas and inspiration can be shared. This type of workplace is likely to have a casual dress code and attract a younger worker. It may be acceptable to work from home and flexible work hours might be offered.
Some large corporations that rely on their web presence for a lot of their business may have in-house web designers and this kind of workplace is likely to be a bit more traditional.
A lot of web designers do freelance work and will work from home. Their home office will be set up entirely as they choose although they may have to be prepared to travel to consult with clients and work environments may vary, depending on the type of client or company they are working with. This option gives a lot of freedom with regard to working hours and locations and is a great option if it is available.