Project websites - Increasing visibility or wasting time?
This answer is from computer science rather than the social sciences. However, I am not sure whether the difference matters much in this context.

Generally, project web sites are done for the following reasons:


Provide a central entry point for a given research endeavour that one can point interested people to (e.g., at conferences). Many projects lead to dozens and dozens of small and large publications distributed over many project partners, so the website of the project collects and often summarizes the main outcomes in a way that is easier to digest.
Advertise the project. It is hard for a project to be successful if nobody knows that the project exists. A website is an easy means to give a "face" to an otherwise pretty amorphous construct.
In some cases, websites have an internal, password-protected area, which the project partners use to exchange documents, discuss in forums, etc. So the website if also a sort of collaboration tool for project partners.
Last but unfortunately not least, project website are often simply a deliverable that the funding agencies expect / require, so they need to be done no matter if it having one serves any concrete goal outside of its mere existence.


That being said, there are of course plenty of websites that are simply useless. The thing is, it is hard to say in advance whether a website will actually be useful for a specific project or not. You may often think in the beginning of the project that you will need a website e.g., as a discussion and dissemination platform, but then nobody ends up using it and it slides into general uselessness.

To answer your questions:


  Are they an effective means to increase visibility of projects?


Maybe, but only if they are very well done and linked in a highly visible way. I would say most websites are not particularly effective in terms of visibility, even though this is typically one of the main goals.


  Under which circumstances does it make sense to set up such a website?


I will always set up at least a rudimentary website. Doing a simple website is close to no effort, and having one (even a simple one) is usually better than having none at all.


  What makes such a website a good website?


This is hard to answer without knowing what specifically the website should do for a project. I assume you mean primarily as a dissemination tool - in that context, what you really need is high-quality content (which is targeted at whatever your audience is), fresh content (try to have a regular schedule, e.g., a monthly research blog), personal touch (photos from meetings, opinion pieces, ...), highly visible linking (the way how Google and other search engines work is that they assume that website linked from important websites are also important, so you need to get your website linked from other highly ranked sites, so as to improve your page rank), and pleasing visuals (make sure that your website is technically up to date).