For example, if I revisit a memory of mine where I'm inside a castle and talking to someone, can the present-me explore different parts of the castle meanwhile the past-me continues her conversation? Is that possible?
A Pensieve memory is an exact memory that a wizard can store or revisit. Think of it as a small video -- a moment in time. When you use the Pensieve to revisit a memory, you can only see that which is in the particular memory. So, if, for example, you have a memory of walking out of the Great Hall and looking about for a moment, that is all you will be able to see. You would not be able to venture further than the memory's confines. Pensieves are not Time-Turners and don't have to do with time, so there is no "present" and "past" me, should I use a Pensieve. There is only one you, and it would be like watching a video of a memory that, for whatever reason, was important to the one storing it. So, the answer to your question is no, you cannot go exploring further than the boundaries of the original memory.
MA: One of our Leaky “Ask Jo” poll winners is theotherhermit, she’s 50 and lives in a small town in the eastern US. I think this was addressed in the sixth book, but, “Do the memories stored in a Pensieve reflect reality or the views of the person they belong to?”
JKR: It’s reality. It’s important that I have got that across, because Slughorn gave Dumbledore this pathetic cut-and-paste memory. He didn’t want to give the real thing, and he very obviously patched it up and cobbled it together. So what you remember is accurate in the Pensieve.
ES: I was dead wrong about that.
ES: I thought for sure that it was your interpretation of it. It didn’t make sense to me to be able to examine your own thoughts from a third-person perspective. It almost feels like you’d be cheating because you’d always be able to look at things from someone else’s point of view.
MA: So there are things in there that you haven’t noticed personally, but you can go and see yourself?
JKR: Yes, and that’s the magic of the Pensieve, that’s what brings it alive.
ES: I want one of those!
JKR: Yeah. Otherwise it really would just be like a diary, wouldn’t it? Confined to what you remember. But the Pensieve recreates a moment for you, so you could go into your own memory and relive things that you didn’t notice the time. It’s somewhere in your head, which I’m sure it is, in all of our brains. I’m sure if you could access it, things that you don’t know you remember are all in there somewhere.
Exclusive Interview (Part Three) with Mugglenet and J.K. Rowling - 07.16.05 - Topic: Pensieves
Let me clarify what I wrote above. Jon Story is correct in his comment. When I said "you are limited to the confines of the memory" I meant to convey the fact that the memory is limited to what was originally viewed. However, that doesn't mean you can't explore within the boundaries of a given memory, multiple times if you wish, and perhaps notice something new within that memory each time you revisit it. So, while you can explore within a memory, what you cannot do is build onto an existing memory -- for example, exploring all of Hogwarts in a memory that was originally confined to the kitchens and House-elves. I hope this makes my answer more clear.
One must generally remain close to the person whose memory it is:
Harry looked anxiously behind him again. Snape remained close by, still buried in his examination questions; but this was Snape’s memory, and Harry was sure that if Snape chose to wander off in a different direction once outside in the grounds, he, Harry, would not be able to follow James any farther.
—Harry Potter and the Order of the Phoenix
While admittedly this is merely Harry's guess, it is an educated one.
As indicated in the other answers, Rowling seemed to indicate that everything in a memory is something that was perceived, whether consciously or subconsciously, which lends a great deal of credence to Harry's supposition.
The answer is no. You cannot explore about a place in a memory, because you didn't actually see anywhere else but your surroundings. You cannot go along a corridor that you have never seen before, can you? Think of watching a video of you, one year ago, sitting in a living room. If you never got up to look into another room, how could you know what it looked like when you revisited? You couldn't because it never happened! The memory is only in which you used your senses at that time.