Where is the option to configure port mappings in the new Microsoft Azure portal (http://portal.azure.com)?
If you're setting up a Classic Virtual Machine (that is, with the legacy APIs, available in both the new and old portals), you'll find the settings under Endpoints, when you look at your VM's settings:
If you created a VM using the new Resource Manager (either via portal or via ARM script), the concept of Endpoint no longer exists. Instead, you have an IP address, associated with a NIC. And that NIC is inside a Network Security Group (NSG). In the NSG, you define inbound and outbound port rules. A few more clicks away, but...
First look at your VM's settings and navigate to the network interface:
Then navigate to the network security group:
Finally, edit the inbound rules:
Note: You may also add outbound rules.