Edit /etc/dhcp3/dhclient.conf
NOTE: You may need to modify /etc/dhcp/dhclient.conf instead of /etc/dhcp3/dhclient.conf
Then find the following line
#prepend domain-name-servers 127.0.0.1;
And change it to
prepend domain-name-servers 8.8.8.8;
This will make dhclient (the DHCP client that NetworkManager uses) prepend this to your dns servers, so resolve.conf will end up looking like this
nameserver 8.8.8.8 nameserver 192.168.1.1
This solution will work everywhere and you will always get the DNS that you have chosen as the primary one.