What is the meaning of "I didn't go to the moon... distance between two places--"?
The full line is, "I didn't go to the moon, I went much further--for time is the longest distance between two places--"
In Tom's final speech at the play's conclusion, he speaks as narrator, the older Tom who had lived the events and looked back upon them. He begins his speech with the passage you mention.
Tom's reference to going to the moon recalls his mother's last words to him: "Go, then! Then go to the moon--you selfish dreamer!" As he says, he did not go to the moon, but he left St. Louis and travelled a great deal, sometimes finding himself alone at night in strange cities. For Tom, time itself is "the longest distance" because physical distance proves to be meaningless to him in his efforts to escape his past. Regardless of the location of the strange city in which he finds himself physically, a part of him is still in the shabby apartment in St. Louis where he last saw Laura. The irony of Tom's life lies in his attempts to escape. He leaves his mother and sister behind to be free and to find his own life. Once he has escaped his miserable life in St. Louis, however, he finds that he will never be free, and he will never make a new life. He will remained trapped by his memories.
Tom here is indirectly implying that he has never gone back to St. Louis to see his mother and Laura. The best way I can think to explain the particular phrase you quoted is to think about childhood friends; though they may actually live in geopaphical proximity to you, if you haven't seen them in years and years, you are actually more seperate and more distanced from them than any amount of miles could ever cover.
Tom's prolonged absence from Laura/his mother's life is the largest distance that he could put between them, greater than just physical location.
This makes the rest of the passage even more tragic; though he has covered the ultimate "distance" by never entering Laura/his mother's life again, he cannot forget them. Though he longed so desperately to start his own life, to live an adventure, to "move" instead of "watching movies", he couldn't ever forget his unserved bond to his family. He remembers Laura in any piece of glass, in awindow, with a familiar bit of music...though he's gone a long time without seeing her, and probably traveled far away, he cannot truly escape her or his bond to her.