Wireless Security Question

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If I have my laptop computer in an airport operating wirelessly, and if some wireless guru is monitor my traffic, he can certainly see the URLs of the web sites that I visit. The router logs for the airport connection would certainly contain my browsing history. If I were to connect to my home computer by RDC and browse through it instead, what would the hacker be able to see? Just that there is a connection to another computer? What would the airport's router logs show?

While I'm not overly concerned with security since there is not much in my browsing history that would interest very many people, there are some occasions when I have to log into web sites (such as cPanel on my shared server) that do not have the https protocol, or whatever it is called. If RDC is secure, it seems like a better solution than subscribing to a proxy service, which I really don't understand anyway.
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