I have read that numerous high frequency trading firms build datacenters near equity exchanges to minimize the milliseconds necessary to get quotes and execute trades. In the case of buying and selling Bitcoin, is my broker's proximity to an exchange relevant? Have we seen Bitcoin brokers start to advertise trade execution guarantees?
Right now, generally no. As far as I know Bitcoin exchanges dont offer peering services, and they all use CDNs (like Incapsula) to prevent DDoS attacks. So moving closer to them isnt going to help much, because you're still going to have all your traffic pass through the CDN. If you were located in China and wanted to access a US exchange, then yes it would help a some, but if you're an American trying to access an American exchange, the lower latency would be negligible.
There aren't really Bitcoin brokers as there are stock brokers. With Bitcoin you generally deal with the exchange yourself, there isnt a middle man like a brokerage. The closest thing I know of to a broker in Bitcoin is BTX Trader, which will purchase coins for you at the best price from multiple exchanges.