I would like to trade forex, but I can only do so from 18:00 until 06:00 (GMT). I have heard that there are times when it is not advisable to trade forex. Do any of those times fall in this window? Are there any commonly accepted "best" times to trade in this window?
I suspect that the times you are referring to are those times when there is relatively low volumes of foreign exchange trading. Lower volumes of trading make it possible for large orders to have a disproportionate effect on the market price. This implies that the times to avoid will be the times with the lowest relative volumes. This will occur on the cusp between the New York market winding down and the Asia/Tokyo market revving up. This will be in the hours preceding Tokyo's opening at 06:00 Tokyo time, so the time to avoid is about 04:00-06:00 Tokyo time, or about 20:00-22:00 GMT (if I've worked out the time difference correctly).
Foreign exchange is a 24 hour, global market. Although each of the three main trading centres - London, New York, Asia - will operate 24 hours a day, they will maintain only a skeleton staff outside of normal working hours. The time difference between London and New York is only 5 hours, so there is no period of time when both centres are operating with a skeleton staff. The time difference between London and Tokyo is 8 hours, so again there is no period of time when both centres are operating with a skeleton staff. The time difference between New York and Tokyo is 13 hours. This does include a period where both centres are operating with a skeleton staff, as well as London operating on a skeleton staff.
Thus, in the couple of hours immediately preceding Tokyo's opening for the regular trading day there is minimal coverage in each of the three main trading centres. As mentioned above, this is the time when large orders can have a disproportionate effect on fx rates and so this is the time to avoid.
Recently I did some experiments with EUR/USD cross and, according to my findings it turned out that the maximum volatility occurs in the range 9-12AM (EST). Each currency pair has its own "top volatility" time window, so it really depends on what you want to trade.
It really depends on your specific goals.
Since you are considering trading FOREX, I assume you hate money. It's more efficient to withdraw your money from the bank and light it on fire.
Perhaps you like trading FOREX like some old ladies like to gamble away their social security checks. Well then its impossible to answer your question as it is based upon personal preference.
Because you are new to forex trading, you would be wise to trade long-term and not short-term. For example, watch the Daily and Weekly charts for trends, not the 15 Minute and 1 Hour.
Doing this, there is little concern for the best time of day. You will ideally have trades setup many days in advance, just waiting for them to be triggered. It doesn't really matter if you're present or not.