Ping time between servers in same data center

I tested the ping times of some of my servers in various situations and while I can't guarantee anything here will improve the latency for your particular use case, here are my best answers to your questions:

Does VPC help with performance at all? My concern is not privacy, only performance.

I tested my servers using a VPC in LAX. I did not see any improvement in ping times using the VPC IP compared to using the Public IP. I tested a standard private IP as well. The best results I saw were from the public IP with no VPC.

Once Affinity is supported, will this help with performance?

Once affinity is supported for Placement Groups, this should help limit latency for applications that are particularly sensitive to it. This does come with increased likelihood of downtime as the machines will share more infrastructure. If two machines are on different hardware but in the same Data Center, the entire Data Center would need to be struggling before they would both have downtime (or there would have to be some bad luck at play). If two machines are, for example, on the same host, that host is now a single point of failure for both.

Are any data centers faster than any others?

I'm not aware of there being anything documented about this, but it's certainly possible there could be small differences. I would think our newer data centers may have improved performance over some of the legacy DCs, but I've never seen specific data about ping times to say for sure. I tested a few and saw very similar results, but I think you'd need to do some testing with your application to see if one provided you better results than others.

Is there any other way to improve latency between servers?

The best results I saw came when using a VLAN. I didn't expect it to help since the VPC didn't help, but it did drop the average ping time for me between two of my servers in Miami.

Here is what I saw with the public IP:

100 packets transmitted, 100 received, 0% packet loss, time 101343ms
rtt min/avg/max/mdev = 0.266/0.413/0.864/0.118 ms

Here is what I saw between the same 2 servers using the VLAN:

100 packets transmitted, 100 received, 0% packet loss, time 101372ms
rtt min/avg/max/mdev = 0.013/0.061/0.311/0.043 ms

I hope that helps. You will likely need to do some testing with your application to get real world data, but from my test with mostly new servers I spun up for this purpose, it might be worth trying a VLAN.