Don't mess with your subnet or MTU. Use "down for everyone or just me", ping the website, that kind of thing. If it happens regularly call your ISP support.
+if you want to see one of the sites you ISP is not delivering try a free web proxy. Slow as but if it's just text it's a way. + log issues with web address and time/date. It's always possible your ISP does not know short changed somewhere and will want to fix the problem.
One thing no one seems to have mentioned is that you might be having a DNS cache issue on the machine in question. Since you are using Safari I will assume you are on a Mac so here is a URL to a site that tells you how to flush the DNS cache when you come up against this problem: http://www.hongkiat.com/blog/how-to-clear-dns-cache-in-mac-osx-leopard/
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