You wouldn’t normally ever connect the hub to your PC. You may on occasion connect the remote to the PC when using the MyHarmony software, to either do a firmware update or to synchronise any configuration changes, but the need for this is decreasing significantly as well, as Logitech have improved the ability to do most updates “over the air” and not require the remote to be physically connected.
Proximity of the Harmony (remote or hub) to the SmartThings hub is not an issue (in fact, further away is probably better, so the Harmony Hub wifi and SmartThings hub Zigbee don’t interfere with each other).
The way the elements connect is as follows:
Harmony Remote <–RF_Link–> Harmony Hub <–WiFi–> Your home router <–Internet–> Logitech Cloud Service <-- Internet–> SmartThings Cloud Service
So, the Harmony never actually talks directly to your SmartThings hub.
If you set up a SmartThings trigger for a Harmony action (e.g. door opens, turn on TV), the events go like this:
SmartThings multisensor sends Zigbee message to SmartThings Hub over
Zigbee mesh network
SmartThings Hub sends message to SmartThings Cloud via your home
router and then the Internet
SmartThings Cloud evaluates message and then executes the Harmony
HarmonyTrigger SmartApp uses Logitech Harmony Hub C2C device type
Logitech Harmony Hub C2C device type (in SmartThings Cloud) talks
(via the Internet) to Logitech Harmony Cloud service
Logitech Harmony Cloud service talks to your Harmony Hub (via the
Internet and your home router)
Your Harmony Hub starts the “Watch TV” activity, sending the
commands to turn on the TV, etc.
Note again how your SmartThings hub and your Harmony hub never talk to each other directly.
The most common causes for people having trouble connecting Harmony to SmartThings seem to be:
Being a user on the new UK servers and therefore currently unable to
use OAuth (required to authenticate you for the SmartThings Cloud
<–> Logitech Cloud communications)
Not having sufficiently up to date firmware installed on their Harmony
Hub and/or Remote.
Having multiple Harmony remotes defined in their Logitech Harmony
(MyHarmony) account, but not having all of those hubs turned on
and connected to the Internet.