Can I allow certain sites that my visitors can browse for free?

You can add sites that your visitors can browse for free in the router admin.

Solution for HotspotWRT / CoovaAP

Go to Hotspot > Access List

Walled Garden Hosts: you can add an IP or hostname here

Walled Garden Domains: you can add a domain name here (all subdomains will be whitelisted)

Solution for DD-WRT

Go to 192.168.20.1 (your router's IP), then go to Services > HotSpot > Additional Chillispot Options.

There are already multiple lines of code there, so scroll at the bottom, press enter and add:

'uamallowed www.yoursite.com,www.yoursite2.com'

Note that the line contains one space only, after the uamallowed word - do not include spaces around the ','-it's important!