Gold for Gems?
Check around midday-pre daily reset. You can see the price change on gems if you look at the graph. Overall if gems are 10g =125gem or higher it is a good time to buy. That tend to happen right before patch day too.
“Quoth the raven nevermore”
Platinum Scout: 300% MF
Check out the Exchange rate charts on GW2Spidy and see if you can spot a pattern with the rate is lowest during the day. Separate weekends and holidays from Monday-Thursday periods.
Problem right now is the daily sales. If something desirable goes on sale or returns, the price will spike up hard. At the very least checking out the daily chart will give you an idea if the current rate is above or below the running 24 hour average.
RIP City of Heroes
First off there is the March sale going on so I would wait to buy them til they go on sale since that will save you a bunch. Past sales had the crystals at 20% off and 25% off, so for the 10 pack instead of 360gems you would need only 288gems (or less if it goes for 25%).
As for when to buy the gems itself is tricky since the sale is making the rate jump all over. You probably want to exchange the gold →gems before that day since the Crystals are a popular item and it might spike that day. Like Behllagh said Spidy can help you spotting daily trends or seeing what the month average is. Overall if I was exchanging right now, I would bite the bullet if I can get 100gems for ~8.4 gold (that’s around 25g for the 288 gems).