Diagnosing network latency issues

Speed of Light:
You are not going beat the speed of light as an interesting academic point. This link works out Stanford to Boston at ~40ms best possible time. When this person did the calculation he decided the internet operates at about "within a factor of two of the speed of light", so there is about ~85ms transfer time.

TCP Window Size:
If you are having transfer speed issues you may need to increase the receiving window tcp size. You might also need to enable window scaling if this is a high bandwidth connection with high latency (Called a "Long Fat Pipe"). So if you are transferring a large file, you need to have a big enough receiving window to fill the pipe without having to wait for window updates. I went into some detail on how to calculate that in my answer Tuning an Elephant.

Geography and Latency:
A failing point of some CDNs (Content Distribtuion Networks) is that they equate latency and geography. Google did a lot of research with their network and found flaws in this, they published the results in the white paper Moving Beyond End-to-End Path Information to Optimize CDN Performance:

First, even though most clients are served by a geographically nearby CDN node, a sizeable fraction of clients experience latencies several tens of milliseconds higher than other clients in the same region. Second, we find that queueing delays often override the benefits of a client interacting with a nearby server.

BGP Peerings:
Also if you start to study BGP (core internet routing protocol) and how ISPs choose peerings, you will find it is often more about finances and politics, so you might not always get the 'best' route to certain geographic locations depending on your ISP. You can look at how your IP is connected to other ISPs (Autonomous Systems) using a looking glass router. You can also use a special whois service:

whois -h v4-peer.whois.cymru.com "69.59.196.212"
PEER_AS | IP               | AS Name
25899   | 69.59.196.212    | LSNET - LS Networks
32869   | 69.59.196.212    | SILVERSTAR-NET - Silver Star Telecom, LLC

It also fun to explore these as peerings with a gui tool like linkrank, it gives you a picture of the internet around you.

Cisco switches puts ICMP at the bottom of the priority list. We get the same results if we ping a busy 3750-X.

You need to look at the system utilization on the switches, as I suspect they are so busy that they are doing software processing of packets. Are you running any kind of layer 3 services on these?

There is a quite serious bug in IOS 12.2.53:

CSCth24278 (Catalyst 2960-S switches)

The CPU utilization on the switch remains high (50 to 60 percent) when the switch is not being accessed by a telnet or a console session. When you telnet or console into the switch, the CPU utilization goes down.

There is no workaround.

Upgrade to 12.2.58-SE1 or later to fix this situation.