Here's a slightly truncated portion of the cut Biggs scene as it appeared in the script. I've highlighted the relevant parts:
LUKE: Look who's talking. Now that you've been around those giant starships you're beginning to sound like my uncle. You've gotten soft in the city...
BIGGS: I've missed you kid.
LUKE: Well, things haven't been the same since you left, Biggs. It's been so... quiet.
Biggs looks around then leans close to Luke.
BIGGS: Luke, I didn't come back just to say good-bye... I shouldn't tell you this, but you're the only one I can trust... and if I don't come back, I want somebody to know.
Luke's eyes are wide with Biggs' seriousness and loyalty.
LUKE: What are you talking about?
BIGGS: I made some friends at the Academy. (he whispers) ...when our frigate goes to one of the central systems, we're going to jump ship and join the Alliance...
Luke, amazed and stunned, is almost speechless.
LUKE: Join the Rebellion?! Are you kidding! How?
BIGGS: Quiet down will ya! You got a mouth bigger than a meteor crater!
LUKE: I'm sorry. I'm quiet. (he whispers) Listen how quiet I am. You can barely hear me...
Biggs shakes his head angrily and then continues.
BIGGS: My friend has a friend on Bestine who might help us make contact.
LUKE: You're crazy! You could wander around forever trying to find them.
BIGGS: I know it's a long shot, but if I don't find them I'll do what I can on my own... It's what we always talked about. Luke, I'm not going to wait for the Empire to draft me into service. The Rebellion is spreading and I want to be on the right side -- the side I believe in.
...................................................................................................................
LUKE: I wish I was going... Are you going to be around long?
BIGGS: No, I'm leaving in the morning...
LUKE: Then I guess I won't see you.
BIGGS: Maybe someday... I'll keep a lookout.
LUKE: Well, I'll be at the Academy next season... after that who knows. I won't be drafted into the Imperial Starfleet that's for sure... Take care of yourself, you'll always be the best friend I've got.
So from this scene we learn that Biggs has been away in the big city (Mos Eisley?) at the Academy. An earlier portion I left out is that he received his commission and is the first mate aboard a ship. He fears being drafted into the Empire so he plans to jump ship and head to the planet Bestine where he hopes to find a Rebel contact. Now, if this was an Imperial Academy why would he be afraid of being drafted into the Empire if he'd already joined it?
So what did the EU take away from all of this? That Biggs left Tatooine to join the Imperial Academy on Prefsbelt IV. And that Bestine is a small town on Tatooine. *face palm*