As stated before, you can edit the hosts file (or update a local DNS server), so that the names point to the desired ip addresses. Some browsers have trouble with cookies when there's no DOT in the name, so you may want to do something like mysites.local
or mysites.ivor
If there's something else running on port 80, You have to configure that server to proxy the requests to IIS (on port 80). If you can't run anything on port 80, you can configure the names, but you'll still need the port at the end.
If only IIS is running, you can set this up by using virtual hosts. You add a binding to the IP address, on port 80, to the DNS name you specified. You can run them all on one port as long as they have different host names.