People visit the graves of their loved ones for a variety of reasons: Some go because they feel more connected. They sit in silence or talk as if the deceased were there listening to them. Others go to remember their loved ones on important dates.
Determining the best day depends entirely on your reason and whether you want to go when the cemetery has few visitors.
Any Day - For starters, to be clear, any day can be the "best" day. Obviously, you might prefer to go on a sunny day rather than a rainy one. You should also consider going when the cemetery's maintenance staff is not performing cleanup and landscaping duties, such as lawn mowing, as they can cause a noisy distraction.
Birthdays - Another option is the person's birthday or your own birthday. If you aren't celebrating with others, you might find comfort visiting the grave of a loved one on a day that marks another year of living. If you're celebrating a person's birthday as a sign of respect, then the perfect day is that person's birth date.
Anniversaries - If the person was your spouse or partner, or your important couples like your parents, grandparents, etc., you might also go on the date of their wedding anniversary. You might also go on the anniversary of the person's death, as that date also holds incredible significance -- visiting the gravestone and perhaps sitting beside it and talking aloud might help when dealing with feelings of depression and loss.
Holidays - There are several big holidays during which it is socially expected for people to visit graves. For example, Memorial Day, Veterans Day and Independence Day are the best days to go when visiting the grave of someone who served in the military. During these holidays, the families and friends of service men and women are expected to show their respect. Additionally, there are usually events held at cemeteries in remembrance of those who died serving their country, such as gun salutes and speeches. The most important reason to go on these holidays is because you are given the opportunity to be around other people who have experienced similar loss.
Weekdays - Lastly, if you do not like crowds, the best day to go to visit loved ones in general is any weekday morning. A lot of people during the week are too busy with work to visit cemeteries -- especially around 9 a.m. to 10 a.m. On the other hand, if someone chooses to go during a work week, then they are more likely to go during a lunch break, or before or after their work shift ends.
A grave in a cemetery is not merely the location where your loved one's body rests. It is a place designed to also give peace to the living. The best day will always be the one that brings you the most comfort and peace.