With the following code I can connect to mysql:
localhost is special cased and uses UNIX sockets instead of TCP/IP.
127.0.0.1 doesn't get that special handling.
See the documentation:
On Unix, MySQL programs treat the host name localhost specially, in a way that is likely different from what you expect compared to other network-based programs. For connections to localhost, MySQL programs attempt to connect to the local server by using a Unix socket file. This occurs even if a --port or -P option is given to specify a port number. To ensure that the client makes a TCP/IP connection to the local server, use --host or -h to specify a host name value of 127.0.0.1, or the IP address or name of the local server. You can also specify the connection protocol explicitly, even for localhost, by using the --protocol=TCP option.
If it doesn't work when you use TCP/IP then the database probably isn't listening on the network. This is generally a good thing as it enhances security (not that listening on 127.0.0.1 exposes any problems, but listening on all interfaces gives more opportunity for attacks).
If you really want to allow connections via the network, then see skip-networking.