How to force the devices connected to the wireless router to open a web site hosted in a local webserver

You could do this if you had wifi gear that supported redirecting all requests to an auth page and then just make the auth page your menu instead of the actual auth page. The problem with this is that many phones will only use the wifi connection when both wifi and 3g/4g is available.

I know that I would avoid a place that hijacked my connection like that and I was forced to change settings on my phone to browse the web.

You can hack things together with DHCPd, IPTables/IPFW/pf and some creative CGI or PHP scripts, but the traditional thing to do is to get a pre-built solution like the one from BlueSocket. Less work / maintenance long-term.